Eurex Clearing Prisma

User Guide: Methodology Description

Final Version © Eurex 2012

Deutsche Börse AG (DBAG), Clearstream Banking AG (Clearstream), Eurex Frankfurt AG, Eurex Clearing AG (Eurex Clearing) as well as Eurex Bonds GmbH (Eurex Bonds) and Eurex Repo GmbH (Eurex Repo) are corporate entities and are registered under German law. Eurex Zürich AG is a corporate entity and is registered under Swiss law. Clearstream Banking S.A. is a corporate entity and is registered under Luxembourg law. U.S. Exchange Holdings, Inc. and International Securities Exchange Holdings, Inc. (ISE) are corporate entities and are registered under U.S. American law. Eurex Frankfurt AG (Eurex) is the administrating and operating institution of Eurex Deutschland. Eurex Deutschland and Eurex Zürich AG are in the following referred to as the “Eurex Exchanges”. All intellectual property, proprietary and other rights and interests in this publication and the subject matter hereof (other than certain trademarks and service marks listed below) are owned by DBAG and its affiliates and subsidiaries including, without limitation, all patent, registered design, copyright, trademark and service mark rights. While reasonable care has been taken in the preparation of this publica- tion to provide details that are accurate and not misleading at the time of publication DBAG, Clearstream, Eurex, Eurex Clearing, Eurex Bonds, Eurex Repo as well as the Eurex Exchanges and their respective servants and agents (a) do not make any representations or war- ranties regarding the information contained herein, whether express or implied, including without limitation any implied warranty of mer- chantability or fitness for a particular purpose or any warranty with respect to the accuracy, correctness, quality, completeness or timeliness of such information, and (b) shall not be responsible or liable for any third party’s use of any information contained herein under any circumstances, including, without limitation, in connection with actual trading or otherwise or for any errors or omissions con- tained in this publication. This publication is published for information purposes only and shall not constitute investment advice respectively does not constitute an offer, solicitation or recommendation to acquire or dispose of any investment or to engage in any other transaction. This publication is not intended for solicitation purposes but only for use as general information. All descriptions, examples and calculations contained in this publication are for illustrative purposes only. Eurex and Eurex Clearing offer services directly to members of the Eurex exchanges respectively to clearing members of Eurex Clearing. Those who desire to trade any products available on the Eurex market or who desire to offer and sell any such products to others or who desire to possess a clearing license of Eurex Clearing in order to participate in the clearing process provided by Eurex Clearing, should con- sider legal and regulatory requirements of those jurisdictions relevant to them, as well as the risks associated with such products, before doing so.

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Final Version

Table of Contents

1 Introduction of Eurex Clearing Prisma...... 5 1.1 Benefits for the Clearing Members and the Clearing House ...... 5 1.2 Margin Components ...... 6 2 Calculation of the Mark to Market Margin ...... 7 2.1 Premium Margin ...... 7 2.2 Current Liquidating Margin ...... 7 2.3 Variation Margin ...... 7 3 Calculation of the Initial Margin...... 9 3.1 Definition of Liquidation Groups and Liquidation Group Splits ...... 10 3.2 Representative Instruments for Exemplary Calculations ...... 11 3.3 Calculation of the Pure Market Risk Component...... 12 3.3.1 Definition of Historical Scenarios...... 12 3.3.2 Definition of Stressed Scenarios ...... 13 3.3.3 Calculation of the P&L based on the defined Scenarios ...... 14 3.3.4 Calculation of Market Risk Measure for Filtered Historical and Stressed Scenarios. . 17 3.4 Calculation of Model Error Adjustments for the Market Risk Component . . . . 22 3.4.1 Correlation Break Adjustment ...... 22 3.4.2 Compression Error Adjustment ...... 26 3.5 Calculation of the Liquidity Risk Component ...... 28 3.5.1 Calculation of Liquidity Risk Component for a single Position...... 29 3.5.2 Aggregation of the Liquidity Risk Components for a Liquidation Group Split . . . . 30 3.6 Putting all Components Together ...... 34 4 Additional Explanations & Special Cases ...... 38 4.1 Special Treatment of Interest Rate Swaps ...... 38 4.2 Treatment of Foreign Currency Risk ...... 38 4.3 Special Treatment of Instruments Close to Expiry ...... 40 5 Margin Replication ...... 41 5.1 Information Provided by Eurex Clearing ...... 41 5.1.1 Overview File Structure ...... 42 5.1.2 Theoretical Prices and Instrument Configuration ...... 43 5.1.3 Risk Measure Configuration ...... 44 5.1.4 Market Risk Aggregation Configuration ...... 44 5.1.5 Market Capacities Configuration ...... 44 5.1.6 Liquidity Factors Configuration ...... 45 5.1.7 Foreign Exchange Rates Configuration ...... 45 5.2 Replication of the Margin Calculation outside Eurex Clearing ...... 45 5.3 Input File Format for Margin Replication...... 45 5.3.1 “Theoretical_Prices_and_Instrument_Configuration” File ...... 46 5.3.1.1 General File Structure ...... 46 5.3.1.2 Fields ...... 47 5.3.1.3 Examples...... 51 5.3.2 “Risk_Measure_Configuration” File ...... 51 5.3.2.1 General File Structure ...... 52 5.3.2.2 Fields ...... 52 5.3.2.3 Example ...... 54 5.3.3 “Market_Risk_Aggregation_Configuration” File...... 54 5.3.3.1 General File Structure ...... 54

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5.3.3.2 Fields ...... 55 5.3.3.3 Example ...... 55 5.3.4 “Market_Capacities_Configuration” File ...... 55 5.3.4.1 Fields ...... 56 5.3.4.2 Example ...... 56 5.3.5 “Liquidity_Factors_Configuration” File ...... 57 5.3.5.1 Fields ...... 57 5.3.5.2 Example ...... 57 5.3.6 “Foreign_Exchange_Rates_Configuration” File ...... 58 5.3.6.1 Fields ...... 58 5.3.6.2 Example ...... 58 5.3.7 End of File marker ...... 59 5.3.7.1 Fields ...... 60 5.3.7.2 Example ...... 61 5.4 Algorithmic Description of the Initial Margin Calculation ...... 61 5.4.1 Step 1: Calculation of Profit and Loss Distributions ...... 61 5.4.2 Step 2: Calculation of the Market Risk Components for all Liquidation Groups . . 63 5.4.3 Step 3: Calculation of the Correlation Break Adjustment ...... 63 5.4.4 Step 4: Calculation of the Compression Error Adjustment ...... 65 5.4.5 Step 5: Calculation of the Liquidity Risk Component ...... 65 5.4.6 Step 6: Calculation of the Initial Margin Figures...... 67 5.4.7 Step 7: Aggregation of the overall Initial Margin Figure ...... 68 6 Appendix ...... 69 6.1 Related Documents and Files ...... 69 6.2 Calculation of VaR Figures ...... 69 6.3 Rounding and Precision of Margin Figures...... 71 6.4 Calculation of the Median ...... 71 6.5 Interpolation of Liquidity Factors ...... 72 6.6 Additional Files ...... 73 6.6.1 “Asset_Class_Information” File ...... 73 6.6.2 “TTE_Bucket_Information” File ...... 74 6.6.3 “Moneyness_Bucket_Information” File ...... 74 7 Glossary...... 76

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Final Version Introduction of Eurex Clearing Prisma

1 Introduction of Eurex Clearing Prisma

Being an industry leader in Central Counterparty (CCP) risk management, Eurex Clearing intends to set new industry standards by introducing a new “Portfolio Based Risk Management” (Eurex Clearing Prisma) methodology for all cleared products both listed and OTC.

The Portfolio Based Risk Management framework will replace the existing “Risk Based Margining” (RBM) methodology. However, to facilitate a smooth transition for clearing members and their clients during the migration period, both methods (RBM and Eurex Clearing Prisma) will run in parallel. During this timespan clearing members and their clients can choose which methodology to apply per liquidation group.

The new methodology is based on the view of each member's portfolio and has the advantage to account for hedging and cross-correlation effects, thus determining the initial margin requirement on a portfolio level as compared to a product by product view. The single elements in the concept are designed for the adequate and stable computation of risk figures, thus ensuring a forward looking risk methodology that is able to cope with new shocks and changes to the financial markets and that is flexibly adapting to changes in the risk environment.

Eurex Clearing Prisma will also introduce a consistent risk methodology that will apply to all cleared markets covering listed and OTC products. Hence, Eurex Clearing Prisma will allow combining Eurex OTC Clear with Eurex Exchange's listed products, allowing for an efficient initial margin aggregation with offsets for hedged positions.

1.1 Benefits for the Clearing Members and the Clearing House The new methodology will offer the following benefits for our clients and for the clearing house:

 Higher Capital Efficiency:

 More accurate risk netting effects in between listed, and between listed and OTC positions.

 Higher capital efficiency for customers due to risk calculations on a portfolio basis.

 More Accuracy:

 Cross-product scenarios enable consistent way to account for portfolio correlation and diversification effects.

 The risk is calculated at 99% confidence level through a forward-looking component (ini- tial margin) and an adequate holding period in line with the default management process.

 The methodology contains a dynamic volatility model and adjustments for illiquidity and model errors.

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Final Version Introduction of Eurex Clearing Prisma

 Consistent Framework aligned with Default Management Process:

 Consistent risk and liquidation framework for listed and OTC products. Positions deemed suitable for simultaneous liquidation are logically assigned to the same liquidation group split, whereby risk offsets are only granted within the same liquidation group split.

 Robustness:

 The methodology is designed to enable stable margin requirements by introducing a coun- tercyclical component based on stressed periods and adequate input parameters.

 More Flexibility:

 A broader range of instruments is covered with faster time-to-market.

1.2 Margin Components

Liquidity Risk Component

Current Liquidating Margin Market Risk based on Filtered Historical Simulation and Variation Margin Stressed Scenarios Initial Margin

Market Risk Component Model Error Mark to Market Margins Premium Margin Adjustments

Backward looking Present Forward looking

Figure 1: Margin Components

The total margin to be delivered consists of two separate components - the backward looking mark to market margins, which depend on the specific product, and a forward looking initial margin. The mark to market margin quantifies the daily profit and loss fluctuations of positions that have occurred in the past by taking into account the portfolios’ current and previous prices.

The methodology for the calculation of the mark to market margin will remain unchanged under the new framework introduced by Eurex Clearing Prisma.

The initial margin requirement is the forward looking component. It serves to cover potential losses of positions incurred over the holding period after a clearing member's default. The methodology for the calculation of the initial margin is the main focus of Eurex Clearing Prisma and will be significantly different from the old RBM approach.

The new methodology for the calculation of the initial margin and its subcomponents will be illustrated in section 3 of this document.

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Final Version Calculation of the Mark to Market Margin

2 Calculation of the Mark to Market Margin

The methodology for the calculation of the following mark to market margins is not affected by Eurex Clearing Prisma and is not the main focus of this document. Therefore those margins are only mentioned briefly. Further information can be found in the original RBM document [3].

2.1 Premium Margin A premium margin must be deposited by the writer of an option. It covers the potential loss that could be incurred if the clearing house were forced to liquidate the position today. The premium margin is continuously adjusted as the option price fluctuates. In case the potential loss upon liquidation increases, the writer will be obliged to deposit a higher premium margin. If on the other hand, prices fluctuate so that the potential loss upon liquidation decreases, the amount of premium margin to be posted will decrease.

The premium margin is only to be posted by the writer of an option as the purchaser's maximum payout risk has already been fully paid in form of the option premium. The premium margin is credited to the buyer of the option.

Premium margins are calculated for all options with “traditional style premium posting”, such as options on equities and equity indices. Options on futures are subject to “futures-style premium posting” and therefore no premium margin must be posted for those instruments. Instead a variation margin as described in section 2.3 will have to be deposited.

2.2 Current Liquidating Margin A current liquidating margin is collected from buyers or sellers of bonds and equities. The current liquidating margin covers losses that would occur in case a position has to be closed out immediately.

As with the premium margin, the current liquidating margin is re-adjusted daily. Contrary to premium margin, the current liquidating margin is collected from either the buyer or seller, who are obliged to deposit the daily profit and loss depending on the relation of the agreed upon purchase price to the current market price.

2.3 Variation Margin Variation margin (a daily offsetting of profits and losses) occurs as a result of the mark to market procedure used for futures and options on futures. Through variation margin, the gains and losses incurred as a result of the price changes in open positions during a given trading day are offset against each other. In contrast to other kinds of margin, variation margin is not an amount

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Final Version Calculation of the Mark to Market Margin which must be deposited as collateral, but is rather a daily cash settlement of booked debit and credit balances.

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3Calculation of the Initial Margin

The Eurex Clearing Prisma initial margin is a simulation-based VaR methodology using stress- period scenarios, filtered historical scenarios and adjustments to account for correlation breaks, compression errors and illiquidity. The initial margin is a forward looking margin component and therefore quantifies a provision for future potential losses over the holding period of a defaulting clearing member's positions. Under the Eurex Clearing Prisma framework the initial margin is calculated taking into account potential correlation and netting effects for positions within a liquidation group split of a single account. The initial margin figures for the different liquidation group splits and accounts are aggregated according to the methodology used in RBM. The definition of the liquidation groups and the liquidation group splits will briefly be outlined in section 3.1.

The initial margin consists of two main subcomponents - the market risk component and the liquidity risk component. Both components are calculated using profit and loss distributions for the liquidation group splits based on a set of different scenario prices for the underlying instruments.

The definition of the scenario prices can be found in sections 3.3.1 and 3.3.2. The calculation of the profit and loss distributions based on those prices is explained in section 3.3.3. The methodology for the computation of the market risk component (section 3.3) including all associated model error adjustments (section 3.4) and the calculation of the liquidity risk component (section 3.5) are described in detail in the following chapter. The subsequent aggregation into a total initial margin figure is illustrated in section 3.6. The figure below schematically illustrates the process for the determination of a liquidation group split's initial margin. Definition of Liquidation Groups & Liquidation Group Splits Scenario Prices Portfolio Data for Instruments Profit and Loss Distributions for Liquidation Group from Clearing Member Cross Product Scenarios Splits

Position 1 Theo Position 2 e.g. Equity prices Prices

… … Scenario 1 M Pure Market 1 47.34 51.19 Model Error Liquidity Risk 2 45.01 48.14 Risk … Adjustments Component Position N Component S 47.76 49.09

Initial Margin for Liquidation Group Splits

Figure 2: Calculation of a Liquidation Group Split’s Initial Margin

Exemplary calculations are demonstrated based on representative instruments throughout this chapter in order to facilitate the understanding of the new methodology.

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3.1 Definition of Liquidation Groups and Liquidation Group Splits The entire portfolio of a clearing member is most likely not suitable for a single auction due to its heterogeneous structure, size or complexity. Therefore, products and instruments in the portfolio will be split into predefined parts called liquidation groups. Liquidation groups are defined on clearing house level across all respective members. In case of a clearing member default these liquidation groups will be liquidated separately while the positions within a liquidation group are intended to be auctioned together. Expiring positions within each liquidation group will be treated separately as immediate actions have to be performed. Therefore the liquidation groups are further divided into so-called liquidation group splits consisting of expiring and non-expiring positions1. Within the Eurex Clearing Prisma methodology, Eurex Clearing grants margin offsets for positions within each liquidation group split of each account.

To achieve market acceptance and to secure the integrity of the clearing house, transparent and clear criteria for the definition of liquidation groups and liquidation group splits are pre-defined in consultation with the clearing members. Once liquidation groups are implemented, the open positions for which the Eurex Clearing Prisma methodology shall be applied2 are mapped to the corresponding liquidation groups and liquidation group splits. Eurex Clearing assigns new products to an existing, restructured or new liquidation group. These new assignments are discussed with members on a regular basis. The composition of liquidation groups and their splitting will be reviewed periodically by the clearing house in order to ensure its on-going validity and relevance.

1. For more information concerning the treatment of expiring positions, please refer to section 4.3. 2. In the migration period the clearing members can chose if the PRISMA methodology shall be applied for a specific liquidation group.

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3.2 Representative Instruments for Exemplary Calculations The calculation of different initial margin components is illustrated by means of the following representative instruments which are mapped to two distinct liquidation groups and their corresponding liquidation group splits: Instrument Price [EUR] Number Trade Unit Liquidation Group Liquidation Group Split of Value contracts (TUV) DAX Option 1,487.00 1 25 LG1: Large Cap LG1_nexp: Liquidation Equity Derivatives Group 1 (non-expiring) DAX Future 146,925.00 1 1 LG1: Large Cap LG1_exp: Liquidation Equity Derivatives Group 1 (expiring) Bobl-Future 2,223.34 1 50 LG2: Fixed-income LG2_nexp: Liquidation Option derivatives Group 2 (non-expiring) CONF Future 136,188.89 1 1 LG2: Fixed-income LG2_nexp: Liquidation derivatives Group 2 (non-expiring)

Table 1 Example - Instruments

Both liquidation groups have a 2-day holding period in this example3. The DAX Future will expire shortly and therefore belongs to the expiring liquidation group split. All other instruments belong to non-expiring liquidation group splits.

The exemplary calculations as shown in the following sections can be verified in the complementary Excel spreadsheet [4] containing all numbers and the necessary steps for their derivation. All numbers in the following tables are rounded to the last cent. Therefore small deviations between expected numbers and the illustrated numbers are possible. An algorithmic description of the initial margin calculation can be found in section 5.3.6.

3. To facilitate the presentation, a holding period of two days is chosen for the exemplary calculations instead of the usu- ally appropriate holding period of approximately 3-5 days.

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3.3 Calculation of the Pure Market Risk Component

Scenario Prices Profit & Loss Liquidation group ‘ s P/L based History of History of Liquidation group split’s P/L (Filtered Historical) Distributions on n - th n - day scenarios Risk factors Risk factors Based on 1st n-day scenarios Liquidation group ‘ s P/L based VaR 1 m P/L1 n Liquidation group split’s P/L 1 P1 P1 1 P/L1 onSortedBased 1st Liquidationn on - day nth scenariosn-day’ s groupP/ L scenarios Liquidation

VaR 2 Market Risk Component VaR* at 99%

1 m 1 P/Ln VaR P750 P750 P/L750/n 750/n n Group Split’s ScenarioHistory Prices of ProfitHistory & Loss of (Stressed) Distributions LiquidationLiquidation groupgroup split’s’ s P/L P/Lbased Risk factors Risk factors onBased n - th on n - day1st m-day stress scenarios per. scen . 1 m 1 n Liquidation group ’ s P/L based VaR 1 P751 P751 P/L1 P/L SortedLiquidation Liquidation groups groupP/ Lsplit’s ’ P/L 1 th onBased 1st non - day m scenarios n-day- scenarios VaR 2 VaR at 99%

1 m 1 P/Ln P1000 P1000 P/L250/n 250/n VaRnm

Figure 3: Calculation of a Liquidation Group's pure Market Risk Component

The pure market risk component, i.e. without the model error adjustments, is calculated based on tail risk measures in form of VaR figures4 utilizing profit and loss distributions on a liquidation group split level using historical and stressed price scenarios5.

Figure 3 schematically illustrates the calculation of the market risk component for a n-day holding period, which is based on the scenario prices of m instruments consecutively aggregated to profit and loss distributions (more precisely to n subsample distributions) for each liquidation group split.

3.3.1 Definition of Historical Scenarios A set of 750 historical scenario prices is used to calculate hypothetical profits and losses for every instrument6. The historical scenario prices for an instrument are calculated by applying 750 historical returns over the n-day holding period7 to its risk factors and revaluating the instrument leading to the 750 different historical scenario prices.

Instead of using a straightforward Historical Simulation, a Filtered Historical Simulation (see [2] in appendix 6.1) is used to calculate the different scenario prices. The Filtered Historical Simulation has superior statistical properties compared to the standard Historical Simulation.

4. These VaR figures are potentially calculated based on the Robust VaR methodology explained in more detail in section 3.3.4. 5. Additional scenario types beyond stressed and historical scenarios may be introduced in the future at the discretion of Eurex Clearing. 6. The exact number of historical scenarios may change over time at the discretion of Eurex Clearing. In order to give a concise presentation the number of historical scenarios is assumed to be 750. 7. In the exemplary calculations n is set to two days for a more concise presentation of the numbers instead of the usually appropriate holding period of approximately 3 - 5 days.

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Scenario prices based on this extended methodology will be referred to as historical scenarios throughout this document.

In order to mitigate artificial statistical effects such as autocorrelation between the different n-day returns that would significantly impair the validity of the calculated risk figures, the prices are divided into n non-overlapping scenario subsamples - one for each day of the holding period - and the risk figures are calculated independently for each subsample.

All historical scenarios are updated on a daily basis with the latest risk factor returns and the new current price information available leading to a new set of 750 historical prices each time.

A set of exemplary historical scenario prices for the representative instruments are illustrated in Table 2.

Example - Historical Scenarios:

The following table shows the different scenario prices used within the Filtered Historical Simulation and the current price separately for both scenario subsamples for all representative instruments shown in section 3.2. All prices will be provided by Eurex Clearing. The scenario prices are already based on n-day (in case of the illustrated example 2-day) returns in accordance with the holding period for each liquidation group. Each scenario is assigned to one of the n (in case of the illustrated example n=2) scenario subsamples as indicated in the second column of the table. Scenario No. Scenario DAX Option DAX Future Bobl-Future CONF Future Subsamples [EUR] [EUR] Option [EUR] [EUR]1 Current Price - 1,487.00 146,925.00 2,223.34 136,188.89 1 1 1,201.78 145,028.50 2,442.26 133,040.57 2 2 1,464.72 148,711.73 2,232.24 131,398.37 3 1 1,475.83 147,048.72 2,233.13 142,094.48 4 2 1,204.64 144,527.76 2,514.36 137,114.52 … 749 1 1,709.84 142,623.32 2,268.02 129,700.13 750 2 1,436.96 141,444.30 2,484.19 147,968.03

1.The scenario prices for the CONF future are already converted into the clearing currency (in this example the clearing currency is EUR). More details on the currency conversion can be found in section 4.2.

Table 2 Example - Scenario Prices (based on a Filtered Historical Simulation of the n-day returns)

3.3.2 Definition of Stressed Scenarios In order to introduce a countercyclical margin component by taking into account periods of high financial distress and extreme events, 250 stressed prices are also simulated as input for the calculation of further risk figures8. These prices are obtained by jointly simulating n-day returns

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Final Version Calculation of the Initial Margin

for all instruments of a liquidation group based on periods with exceptionally high fluctuations of the corresponding risk factors. In contrast to the calculation of historical scenarios prices no filtering is used for the stressed scenarios.

According to the methodology for the historical scenarios, the stressed scenarios are divided into n non-overlapping, consistent subsamples in order to avoid autocorrelations. As the stressed scenarios are also taken from historical data, the actual correlations between the different risk factors throughout the stressed periods are captured efficiently.

The selection of the stress periods are updated on demand in case new market disruptions need to be taken into account. As the stressed returns are always applied to the current price, the stressed scenario prices are updated at least daily due to the changing current price.

Example - Stressed Scenarios:

The following table shows the stressed scenario prices based on historical 2-day returns during identified stress periods for the representative instruments. Similar to the historical scenario prices the stressed scenario prices are provided by Eurex Clearing. Scenario No. Scenario DAX Option DAX Future Bobl-Future CONF Future Subsamples [EUR] [EUR] Option [EUR] [EUR] Current Price - 1,487.00 146,925.00 2,223.34 136,188.89 751 1 2,865.85 155,156.60 2,661.03 130,145.57 752 2 1,595.15 149,612.03 1,847.51 132,453.30 753 1 2,009.66 148,586.70 2,507.21 126,244.36 754 2 2,006.68 146,298.86 1,917.05 138,731.52 … 999 1 1,286.96 138,912.50 2,328.00 146,835.36 1000 2 1,486.47 151,731.90 2,376.15 140,888.80

Table 3 Example - Scenario Prices (Stressed Simulation)

3.3.3 Calculation of the P&L based on the defined Scenarios The historical and stressed scenario prices are the basis for the profit and loss distribution of the (i) instruments. The profit or loss PLs of an instrument i based on a scenario price (measured in (i ) (i) target currency) under scenario s Ps and the current price P (measured in target currency) is calculated as the difference between the current price9 and the scenario price multiplied by the trade unit value (TUV) of instrument i using the following formula10:

ሺ௜ሻ ሺ௜ሻ ሺ௜ሻ ሺ௜ሻ ൌ ͳ ǥ ͳͲͲͲ ݏ൯ήܷܸܶ௜ǡ ׊ܺܨ௦ െܲ ήܺܨ௦ ൌοܲ௦ ൌ൫ܲ௦ ήܮܲ

8. The exact number of stressed scenarios may change over time at the discretion of Eurex Clearing. In order to give a concise presentation the number of stressed scenarios is assumed to be 250. 9. Also denoted as neutral scenario.

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The profit or loss of a liquidation group split l under a scenario s is calculated by aggregating the profits or losses for every instrument i multiplied by the number of contracts Ni in the respective liquidation group for all instruments i within one liquidation group split l according to the following formula:

௟ ሺ௜ሻ ௦ܮ௟ ܰ௜ ήܲא௦ ൌ σ௜ܮܲ

The calculation of the profits and losses is identical for both filtered historical and stressed scenarios. The profit and loss figures for each scenario subsample are aggregated into one P&L vector per scenario subsample leading to n vectors consisting of 750/n prices for the filtered historical scenarios and another set of n vectors containing 250/n stressed prices11.

Example - Calculation of Profit and Loss Vectors:

The following table shows the profits (given as positive numbers) and losses (given as negative numbers) based on the filtered historical and stressed 2-day scenarios for all representative instruments divided into the two scenario subsamples. The shown profit and losses already take into account the number of contracts and the trade unit value (TUV) for each instrument. Scenario No. Scenario DAX Option DAX Future Bobl-Future CONF Future Subsample Option 1 1 (1,201.78 - -1,896.50 10,946.38 -3,148.31 1,487.00) * 25=-7,130.62 2 2 -556.99 1,786.73 444.99 -4,790.52 3 1 -279.15 123.72 489.53 5,905.59 4 2 -7,059.10 -2,397.24 14,551.07 925.63 … 749 1 5,571.02 -4,301.68 2,234.10 -6,488.76 750 2 -1,250.97 -5,480.70 13,042.63 11,779.14 751 1 34,471.37 8,231.60 21,884.47 -6,043.32 752 2 2,703.72 2,687.03 -18,791.06 -3,735.59 753 1 13,066.56 1,661.70 14,193.70 -9,944.52 754 2 12,991.92 -626.14 -15,314.29 2,542.63 … 999 1 -5,000.90 -8,012.50 5,233.10 10,646.48 1000 2 -13.19 4,806.90 7,640.72 4,699.91

Table 4 Example - Profit and Loss Vectors of the Instruments based on scenario prices obtained from Table 2 and Table 3

10. The FX conversion is done by multiplication or division, depending on the FX rate quotation. FX rates for all combina- tions of product currency and clearing currency are provided in the Foreign Exchange Rates Configuration File (see section 4.2 for details). 11. The exact number of scenario prices might change slightly in order to get vectors of equal length.

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The following tables show the profit and loss distributions for all liquidation group splits. Again the scenarios were divided into the scenario subsamples as indicated by the corresponding column. Scenario Scenario Scenario DAX Option P&L LG1 Non- DAX Future P&L LG1 No. Type Sub- Expiring Expiring sample 1 Historical 1 -7,130.62 -7,130.62 -1,896.50 -1,896.50 3 Historical 1 -279.15 -279.15 123.72 123.72 … Historical 1 … … … … 749 Historical 1 5,571.02 5,571.02 -4,301.68 -4,301.68 751 Stressed 1 34,471.37 34,471.37 8,231.60 8,231.60 753 Stressed 1 13,066.56 13,066.56 1,661.70 1,661.70 … Stressed 1 … … … … 999 Stressed 1 -5,000.90 -5,000.90 -8,012.50 -8,012.50 2 Historical 2 -556.99 -556.99 1,786.73 1,786.73 4 Historical 2 -7,059.10 -7,059.10 -2,397.24 -2,397.24 … Historical 2 … … … … 750 Historical 2 -1,250.97 -1,250.97 -5,480.70 -5,480.70 752 Stressed 2 2,703.72 2,703.72 2,687.03 2,687.03 754 Stressed 2 12,991.92 12,991.92 -626.14 -626.14 … Stressed … … … … … 1000 Stressed 2 -13.19 -13.19 4,806.90 4,806.90

Table 5 Example - Profit or Loss for Liquidation Group 1 - Expiring and Non-Expiring based on Table 4

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Scenario No. Scenario Type Scenario Bob-Future CONF Future P&L LG2 Non- Subsample Option Expiring 1 Historical 1 10,946.38 -3,148.31 7,798.07 3 Historical 1 489.53 5,905.59 6,395.12 … Historical 1 … … … 749 Historical 1 2,234.10 -6,488.76 -4,254.66 751 Stressed 1 21,884.47 -6,043.32 15,841.15 753 Stressed 1 14,193.70 -9,944.52 4,249.18 … Stressed 1 … … … 999 Stressed 1 5,233.10 10,646.48 15,879.58 2 Historical 2 444.99 -4,790.52 -4,345.52 4 Historical 2 14,551.07 925.63 15,476.69 … Historical 2 … … … 750 Historical 2 13,042.63 11,779.14 24,821.78 752 Stressed 2 -18,791.06 -3,735.59 -22,526.65 754 Stressed 2 -15,314.29 2,542.63 -12,771.66 … Stressed … … … … 1000 Stressed 2 7,640.72 4,699.91 12,340.62

Table 6 Example - Profit or Loss for Liquidation Group 2, Non-expiring based on Table 5

3.3.4 Calculation of Market Risk Measure for Filtered Historical and Stressed Scenarios The pure market risk component is primarily based on n-day VaR risk figures utilizing the profit and loss distributions derived from the historical and stressed scenarios12. The VaR figures will be calculated separately for each scenario subsample a for both the filtered historical and the stressed scenarios based on the respective profit and loss vectors of the liquidation group split l13 ௛௜௦௧ ௦௧௥௘௦௦௘ௗ and are subsequently denoted as ܸܴܽ௟ǡ௔ and ܸܴܽ௟ǡ௔ . In order to increase the robustness of the calculated risk measures the n-day VaR for the filtered historical scenarios will be calculated at a confidence level of 95% and subsequently scaled to the desired confidence level of 99% using a scaling factor assuming a heavy-tailed student-t distribution14. The parameters of the t-distribution are set by Eurex Clearing based on an initial calibration and regular validation. A VaR figure scaled in this way is called Robust VaR.

12. More scenario types beyond the historical and stressed scenarios might be introduced in the future at the discretion of Eurex Clearing. Those scenarios will be treated similar to the stressed and historical scenarios. 13. The method to calculate the VaR figures is described in section 6.2. 14. The lower confidence level and the degrees of freedom of the t-distribution may be adjusted at the discretion of Eurex Clearing. Both the lower confidence level and the necessary scaling factor will be provided by Eurex Clearing via the transparency enablers.

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The VaR based on the stressed scenarios is calculated on a 90% confidence level. In accordance to the VaR figures for the filtered historical scenarios an appropriate scaling factor will be applied to scale the stressed VaR to the desired confidence level of 99%.

Example Calculation of VaR for Historical Simulation and stressed Scenarios:

The tail risk measures for each liquidation group split l are calculated separately at the 95% confidence level for every scenario subsample (the colors emphasizes the different subsamples) and subsequently scaled to the 99% confidence level15.

In the following example, the scaling factor for the projection of the VaR figure based on the filtered historical scenarios from a confidence level of 95% to 99% is 1.93 and the scaling factor for the projection of the stressed VaR figure from a confidence level of 90% to 99% is 2.7816.

15. A positive VaR figure indicates a loss. The VaR figures utilized for the calculation of the initial margin will always be bounded by zero. 16. The illustrated values are based on a heavy-tailed student t-distribution with an exemplary 3 degrees of freedom.

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Scenario No. Scenario Type Scenario P&L LG 1 non-expiring Subsample 1 Historical 1 -7,130.62 3 Historical 1 -279.15 … Historical 1 … 749 Historical 1 5,571.02

95%,hist Historical 1 8,392.39 VaR1,1

99%,hist Historical 1 8,392.39*1.93=16,197.31 VaR1,1

751 Stressed 1 34,471.37 753 Stressed 1 13,066.56 … Stressed 1 … 999 Stressed 1 -5,000.90

90%,stressed Stressed 1 11,220.27 VaR1,1

99%,stressed Stressed 1 11,220.27*2.78=31,192.36 VaR1,1

2 Historical 2 -556.99 4 Historical 2 -7,059.10 … Historical 2 … 750 Historical 2 -1,250.97

95%,hist Historical 2 7,327.33 VaR1,2

99%,hist Historical 2 14,141.75 VaR1,2

752 Stressed 2 2,703.72 754 Stressed 2 12,991.92 … Stressed 2 … 1000 Stressed 2 -13.19

90%,stressed Stressed 2 8,548.54 VaR1,2

99%,stressed Stressed 2 23,764.93 VaR1,2

Table 7 Example- VaR Calculation Liquidation Group 1, Non-Expiring based on profit and loss distributions shown in Table 5

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Scenario No. Scenario Type Scenario P&L LG 1, expiring Subsample 1 Historical 1 -1,896.50 3 Historical 1 123.72 … Historical 1 … 749 Historical 1 -4,301.68

95%,hist Historical 1 7,656.30 VaR2,1

99%,hist Historical 1 14,776.66 VaR2,1

751 Stressed 1 8,231.60 753 Stressed 1 1,661.70 … Stressed 1 … 999 Stressed 1 -8,012.50

90%,stressed Stressed 1 7,506.17 VaR2,1

99%,stressed Stressed 1 20,867.16 VaR2,1

2 Historical 2 1,786.73 4 Historical 2 -2,397.24 … Historical 2 … 750 Historical 2 -5,480.70

95%,hist Historical 2 6,894.52 VaR2,2

99%,hist Historical 2 13,306.43 VaR2,2

752 Stressed 2 2,687.03 754 Stressed 2 -626.14 … Stressed 2 … 1000 Stressed 2 4,806.90

90%,stressed Stressed 2 8,187.12 VaR2,2

99%,stressed Stressed 2 22,760.19 VaR2,2

Table 8 Example - VaR Calculation Liquidation Group 1, expiring based on profit and loss distributions shown in Table 5

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Scenario No. Scenario Type Scenario P&L LG 2, non-expiring Subsample 1 Historical 1 7,798.07 3 Historical 1 6,395.12 … Historical 1 … 749 Historical 1 -4,254.66

95%,hist Historical 1 22,119.32 VaR3,1

99%,hist Historical 1 42,690.28 VaR3,1

751 Stressed 1 15,841.15 753 Stressed 1 4,249.18 … Stressed 1 … 999 Stressed 1 15,879.58

90%,stressed Stressed 1 21,184.65 VaR3,1

99%,stressed Stressed 1 58,893.33 VaR3,1

2 Historical 2 -4,345.52 4 Historical 2 15,476.69 … Historical 2 … 750 Historical 2 24,821.78

95%,hist Historical 2 28,068.99 VaR3,2

99%,hist Historical 2 54,173.14 VaR3,2

752 Stressed 2 -22,526.65 754 Stressed 2 -12,771.66 … Stressed 2 … 1000 Stressed 2 12,340.62

90%,stressed Stressed 2 22,270.11 VaR3,2

99%,stressed Stressed 2 61,910.91 VaR3,2

Table 9 - Example - VaR Calculation Liquidation Group 2, non-expiring based on profit and loss distributions shown in Table 6

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3.4 Calculation of Model Error Adjustments for the Market Risk Component In order to mitigate model risk inherent in the calculation of the tail risk measures, several model error adjustments are calculated and added to the pure market risk component described in section 3.3.4.

The following two model error adjustments are introduced:

(1) The correlation break adjustment is introduced to take into account possible non- stationarities such as breaks in the correlations between the risk factors of the instruments, which can greatly reduce the diversification effects between instruments within a liquidation group leading to an underestimation of its actual portfolio risk. (2) The compression error adjustment mitigates potential model errors such as using volatility surfaces as input factors whose dynamics are approximated using principal component analyses or pricing based on benchmark risk factors. If applicable the model error adjustments are calculated and subsequently added to risk measures separately for all scenario subsamples and liquidation group splits.

3.4.1 Correlation Break Adjustment The correlation break adjustment is introduced to account for non-stationarities or market regime changes such as the fact that the correlation structure of the market risk factors may change over time. The market risk measure described in section 3.3.4 implicitly assumes stationary market conditions over all scenarios leading to potentially aggressive risk estimates.

In case of changes in the correlation structure, assumed diversification effects cannot be realized at all times and therefore the risk measure is potentially underestimating a liquidation group split's actual risk as liquidations may be necessary in times of portfolio-adverse correlation regimes.

Therefore, in addition to calculating the risk measure for all historical scenarios of a subsample, each subsample is further divided into several subsets representing different moving time- windows.

The subset risk measures ܸܴܽ௦௨௕ǡ௛௜௦௧ are then recalculated for each stepwise moving time- ௟ǡ௔ǡ்ೕ

window with end-date Tj of every scenario subsample a and every liquidation group split l independently.

These new risk measures are based on the market conditions of the respective subset instead of the implicit market conditions over all scenarios.

Due to changes in market regimes the risk figures vary over the different subsets of each scenario subsample. The following figure illustrates the development of a moving VaR (orange dotted line) over time calculated using scenarios taken from the different time-windows and the VaR calculated based on all scenarios of the full scenario subsample (straight green line).

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Example: -15000

-15500 moving VaR (99%) VaR (99%) -16000 Excess RM -16500 distribution -VaR -17000 CB -17500 Excess risk -18000 17/07/08 17/10/08 17/01/09 17/04/09 17/07/09 End date (mov. window)

Figure 4: Moving VaR vs Full scenario subgroup VaR

The correlation break adjustment is based on the potentially harmful deviations of the risk measures for the sub-windows from their calculated value across the full scenario subsample. These deviations are measured using an excess risk measure.

The excess risk measure ܸܴܽ௦௨௕ǡା for a liquidation group split k and scenario subsample a is ௟ǡ௔ǡ்ೕ defined as the difference between the VaR calculated over the full scenario subsample a ௛௜௦௧ (ܸܴܽ௟ǡ௔ ), which is illustrated as the green line in the figure above, and the moving time-window VaR (ܸܴܽ௦௨௕ǡ௛௜௦௧ ) figures calculated based on different time-windows of this scenario subgroup ௟ǡ௔ǡ்ೕ (shown as the orange data points) conditional on the fact that the moving VaR is strictly more conservative than the average VaR (i.e. the orange data points lie below the straight green line)17.

Formally the excess risk measure ܸܴܽ௦௨௕ǡା for a sub-window ending in T is calculated as: ௟ǡ௔ǡ்ೕ j

௦௨௕ǡା ൌ݉ܽݔሺͲǡܸܴܽ௦௨௕ǡ௛௜௦௧ െ ܸܴܽ௛௜௦௧ሻܴܸܽ ௟ǡ௔ǡ்ೕ ௟ǡ௔ǡ்ೕ ௟ǡ௔

The distribution of the excess risk measure is illustrated on the right hand side of the graph above.

The mean excess risk figure is calculated for every scenario subsample a and for every liquidation group split l separately according to the following formula:

ͳ ௦௨௕ǡା ଶ ܯܧܴ ൌ ට ൗ ା σ ሺܸܴܽ ሻ , ௟ǡ௔ ݊ ்ೕ ௟ǡ௔ǡ்ೕ ௔ ,

ା where ݊௔ is the number of sub-windows whose VaR figure strictly exceeds the VaR for the full scenario subsample a.

17. Both VaR figures (full and moving time scenario subgroup) are calculated at the same confidence level. The utilized confidence level might differ from the confidence level used for the calculation of the market risk component and is provided by Eurex Clearing via the transparency enabler files.

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In order to assure a minimum level for the correlation break and to cap the model error additional bounds relative to the market risk are introduced. The correlation break for each scenario subsample a is therefore calculated according to the following formula: ௛௜௦௧ ௛௜௦௧ ܥܤ௟ǡ௔ ൌ ‹ሺɗ ή ܸܴܽ௟ǡ௔ ǡƒšሺߢήܯܧܴ௟ǡ௔ǡ ߶ ή ܸܴܽ௟ǡ௔ ሻሻ

Where18:

 ψ is the upper bound for the correlation break adjustment relative to the market risk compo- nent of the corresponding liquidation group split and scenario subsample

 Φ is the lower bound for the correlation break adjustment relative to the market risk compo- nent of the corresponding liquidation group split and scenario subsample

 κ is a factor to scale the mean excess risk measure.

For stressed scenario prices no correlation break adjustment is applied.

Example - Calculation of Correlation Break Adjustment:

The following table shows the VaR figures for each liquidation group and time window19: Liquidation Group 1, Liquidation Group 1, non-expiring expiring Scenario Sub- ݐݏݑܾǡ݄݅ݏܴܸܽ ݐݏݑܾǡ݄݅ݏܴܸܽ ݐݏݑܾǡ݄݅ݏܴܸܽ ݐݏݑܾǡ݄݅ݏܴܸܽ window ݈ǡܽǡ݆ܶ ݈ǡܽǡ݆ܶ ݈ǡܽǡ݆ܶ ݈ǡܽǡ݆ܶ Scenario Scenario Scenario Scenario Subsample 1 Subsample 2 Subsample 1 Subsample 2

Sub-window T1 7,342.92 7,102.76 7,088.73 6,650.61

Sub-window T2 6,987.44 7,102.76 7,088.73 6,650.61

Sub-window T3 6,987.44 7,082.52 7,088.73 6,650.61

Sub-window T4 6,987.44 7,082.52 7,088.73 6,650.61 ……………

Sub-window T225 9,473.37 7,517.51 7,770.49 7,390.70

Sub-window T226 9,473.37 7,517.51 7,770.49 7,390.70 Total Scenario 6,336.89 7,327.33 7,656.30 6,894.52 Subgroup

Table 10 Example - Time-window VaR figures of liquidation group 1 for correlation break

18. The parameters ψ, κ and Φ will be changed by Eurex Clearing if deemed necessary based on backtesting results and communicated via the transparency enablers. 19. A 95% confidence level was chosen for the calculation of the sub-window VaR figures and the VaR over the full sce- nario subsample.

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Liquidation Group 2, non-expiring Scenario Sub- ݐǡ݊െ݀ܽݕݏݑܾǡ݄݅ݏܴܸܽ ݐǡ݊െ݀ܽݕݏݑܾǡ݄݅ݏܴܸܽ window ݈ǡܽǡ݆ܶ ݈ǡܽǡ݆ܶ Scenario Scenario Subgroup 1 Subgroup 2

Sub-window T1 20,507.94 25,096.87

Sub-window T2 20,507.94 25,096.87

Sub-window T3 20,507.94 27,681.79

Sub-window T4 20,507.94 27,681.79 ………

Sub-window T225 24,616.47 29,712.72

Sub-window T226 24,616.47 29,712.72 Total Scenario 22,119.32 28,068.99 Subgroup

Table 11 Example - Time-window VaR figures of liquidation group 2 for correlation break

The following table shows the calculation of the correlation break adjustment based on the excess risk measures taken from the table above20: Scenario Sub-window LG 1, nexp Subsample 1 LG 1, nexp LG 1, exp LG 1, exp Subsample 2 Subsample 1 Subsample 2 Mean Excess Risk: 130.28 619.05 443.99 ටͳൗ ܯܧܴ௟ǡ௔ ͳʹͳ

൅ ͳǡͳ͸ͺǡͷʹ͹ǤͲͻሻ ڮ ͳ ௦௨௕ǡା ଶ ή ඥሺͲ ൅ ൌ ൗ ା ෍ሺܸܴܽ ሻ ඨ ݊௔ ௟ǡ௔ǡ்ೕ ൌ ͻͷͺǤʹͳ ்ೕ

Lower bound: 0.00 0.00 0.00 0.00

ଽଽΨǡ௛௜௦௧ ߶ ή ܸܴܽ௟ǡ௔

Upper bound: 12,957.85 11,313.40 11,821.33 10,645.14 ଽଽΨǡ௛௜௦௧ ɗ ή ܸܴܽ௟ǡ௔

Correlation Break 1,849.35 251.43 1,194.77 856.89 Adjustment: CBl,a

20. The lower and upper bound is defined by the following parameters: Φ=0%, ψ=80%.

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Scenario Sub-window LG 2, nexp LG 2, nexp Subsample 1 Subsample 2 Mean Excess Risk: 1,300.86 1,065.55

ܯܧܴ௟ǡ௔

ͳ ௦௨௕ǡା ଶ ൌ ൗ ା ෍ሺܸܴܽ ሻ ඨ ݊௔ ௟ǡ௔ǡ்ೕ ்ೕ

Lower bound: 0.00 0.00

ଽଽΨǡ௛௜௦௧ ߶ ή ܸܴܽ௟ǡ௔

Upper bound: 34,152.23 43,338.51 ଽଽΨǡ௛௜௦௧ ɗ ή ܸܴܽ௟ǡ௔

Correlation Break 2,510.66 2,056.50 Adjustment: CBl,a

Table 12 Example - Calculation of the Correlation Break Adjustment

3.4.2 Compression Error Adjustment The compression error adjustment compensates for errors due to model assumptions, which can in general be attributed to methodological simplifications for reasons of stability and tractability. Such model assumptions comprise for example scenario pricing based on benchmark risk factors, which is necessary if insufficient data is available for the actual risk factor, e.g. in case of a new instrument. Further examples include the application of approximate pricing methods or pricing based on a reduced set of risk factors. In the following, as an example for the compression error adjustment, pricing based on a reduced set of risk factors will be discussed in more detail.

The implied volatility surfaces used for the pricing of options are based on a reduced set of risk factors in order to increase the tractability and improve the statistical stability of the resulting risk scenarios. This procedure significantly reduces the complexity, but preserves the significant part of the inherent risk caused by the variability of the volatility surface. Therefore, although adequacy of risk modeling is guaranteed, the inclusion of a suitable error adjustment enhances the quality of the risk measure.

In the above case, risk factor reduction (or risk factor compression) is achieved by means of a principal component analysis (PCA), where deformations of the volatility surface are represented by changes of a reduced set of dominant risk components of the volatility surface dynamics instead of the actual changes of the whole volatility surface.

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The total n-day compression error for an instrument i will be provided by Eurex Clearing as an ௛௜௦௧ absolute error term for a single contract for both historical (ܥܧ௜ǡ௔ ) and stressed scenario prices ௦௧௥௘௦௦௘ௗ (ܥܧ௜ǡ௔ ) ) for every scenario subsample a. The total compression error adjustments of a liquidation group split l is calculated by aggregating the absolute compression errors for all instruments i of a liquidation group split using the respective number of contracts Ni for both the historical and the stressed scenarios:

௛௜௦௧ ௛௜௦௧ ௦௧௥௘௦௦௘ௗ ௦௧௥௘௦௦௘ௗ ௜ǡ௔ หܧܥ௟หܰ௜ ήܷܸܶ௜ ήא௜ǡ௞ ൌ σ௜ܧܥ ௜ǡ௔ ห andܧܥ௟หܰ௜ ήܷܸܶ௜ ήא௔ǡ௟ ൌ σ௜ܧܥ

In addition to the aforementioned compression error for options due to the risk factor reduction of the implied volatility surface, additional compression error adjustments will also be applied to other instruments (such as futures) in case approximate pricing models, risk factors based on benchmarks or a reduced set of risk factors are utilized.

All compression errors will be provided by Eurex Clearing via the transparency enabler files.

Example - Calculation of the Compression Error Adjustment: Filtered Historical Simulation Stressed Scenarios Instrument Figure Scenario Scenario Scenario Scenario Subsample 1 Subsample 2 Subsample 1 Subsample 2 DAX Compression Error 17.84 23.79 11.90 20.82 Option Number of 25 contracts * TUV Compression Error Adjustment 446.10 594.80 297.40 520.45 Liquidation Group 1, non- expiring DAX Compression Error 0 0 0 0 Future Number of 1 contracts * TUV Compression Error Adjustment 0 0 0 0 Liquidation Group 1, expiring Bobl Future Compression Error 0.13 0.18 0.09 0.15 Option Number of 50 contracts * TUV CONF Compression Error 2.50 6.00 5.50 25.00 Future Number of 1 contracts * TUV Compression Error Adjustment 9.09 14.78 9.89 32.68 Liquidation Group 2, non- expiring

Table 13 Example - Calculation of the Compression Error Adjustment

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3.5 Calculation of the Liquidity Risk Component The liquidity risk component is designed to capture the effect of adverse price movements when liquidating portfolios. The following most important characteristics of these adverse price movements were taken into consideration:

(1) The liquidity risk component depends on the relative size of the position. The liquidity risk component is a function of the position size and the total market capacity, which can be characterized by means of the daily traded volume or an open interest of a financial instrument. (2) The liquidity risk component depends on the current level of market risk in the respective product - i.e. the higher the volatility of an instrument's price, the higher the premium. Therefore the liquidity risk component is modeled as a fraction of the market risk component. (3) Even for the small position sizes, the liquidity risk component is not zero. In reality trading does not actually occur at mid prices, but at bid or ask prices. Therefore the minimum liquidity component is defined by the liquidity premium as specified below. (4) Market capacities and liquidity risk components are product-specific and unevenly distributed across product subgroups - i.e. for options the market capacities and bid-ask spreads depend on their moneyness and time to expiry. . . . . Component . Component . Component Liqui Liqui Liqui Position Size Position Size Position Size

Low Market Risk High Market Risk

Figure 5: Illustration of the Impact of Position Size and Market Risk on Liquidity Risk Component

Figure 5 shows the liquidity risk component’s dependence on the position size and the market risk of three positions with different risk profiles. For all three positions the liquidity risk component is non-zero for a small position size (i.e. on the left hand side of each graph) and grows with an increasing position size. The liquidity risk component for a position carrying a higher market risk increases at a faster rate than the liquidity risk component for positions with a smaller market risk.

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3.5.1 Calculation of Liquidity Risk Component for a single Position The liquidity risk component will be calculated position-wise. The main drivers of the position- wise liquidity risk component are:

 the market risk measure of the position, which captures the volatility of the market,

 the liquidity factor determines the fraction of market risk captured in the liquidity component depending on asset class, position size and market capacity of the instrument, and

 the liquidity premium of an instrument.

For all instruments except for interest rate swaps the liquidity risk component for a position in instrument i is calculated using the following formula21:

ȁܾ݅݀ െܽݏ݇ȁ ௣௢௦ ௣௢௦ǡ௘௙௙ ෙ ௜ ௜ ෙ ܮܥ௜ ൌ ܸܴܽ௜ ήܮܨቀหܰ௜หǡܥቁ൅ሺ ሻหܰ௜ ήܷܸܶ௜ ήܲ௜หǡ ͳͲͲͲͲ כ ௜ȁ݇ݏȁܾ݅݀௜ ൅ܽ

where

௣௢௦ǡ௘௙௙  ܸܴܽ௜ is the market risk measure (i.e. the VaR) calculated in target currency (see sec- tion 4.2) for the net effective position i22

23  LF(|Ňi|,C) is the linearly interpolated liquidity factor given as a function of the absolute net

effective position size |Ňi| (i.e. effective number of contracts) and the market capacity C,

 Ňi is the net effective position size (i.e. effective number of contracts for instrument i multi- plied by the net gross ratio ngr (further information concerning the net effective position size is given in the following paragraphs),

 Pi is the current price for instrument i, measured in target currency (see section 4.2), hence for target currency not equal to instrument currency, price is converted using current FX rate

 TUVi is the trade unit value of instrument i, and

ȁ௕௜ௗ೔ି௔௦௞೔ȁ  is the liquidity premium of the instrument i in basispoints as given in the Transpar- ȁ௕௜ௗ೔ା௔௦௞೔ȁ ency Enabler files.

Typical portfolios comprise long and short positions in instruments, which are quantitatively exposed to the same risk drivers. In such a risk bucket, only the total net exposure of the offsetting positions will be hedged in case of a liquidation. Therefore, instead of using the number of contracts to calculate the position-wise liquidity components, an effective position size

21. The liquidity risk component for interest rate swaps is calculated using a modified version of this methodology, which is not in scope of this document. 22. The instrument VaR figures will be provided for all necessary target currencies by Eurex Clearing. For each instrument two figures are delivered, one to be used for long positions and one for short positions, since returns for nonlinear instruments are not distributed symmetrically. The positional VaR figures are calculated based on the net effective po- sition size of the clearing member taking into account the trade unit value. 23. The interpolation of the liquidity factors is described in the appendix (section 6.3).

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is calculated reflecting possible risk netting over products with similar risk structure. The definition of the risk buckets is based on instrument specific characteristics such as the time to expiry and - for options - the modified moneyness24.

The effective position size is calculated using the net gross ratio of a risk bucket, which is computed according to the following formula:

σ ܰ ݊݃ݎ ൌ ቤ ௜ఢோ௜௦௞஻௨௖௞௘௧ ௜ ቤ σȁ௜ఢோ௜௦௞஻௨௖௞௘௧ ܰ௜ȁ

The net effective position size Ňi for position in instrument i is then given as:

ܰෙ௜ ൌ݊݃ݎήܰ௜

where:

25  Ňi is the position size (i.e. number of contracts) of instrument i .

The liquidity factors are given by a lookup table depending on the absolute value of the net effective position size relative to the market capacity for each asset class.

The market capacities and liquidity premiums will also be provided using lookup tables. The dimensions of these tables are specified by product class, e.g. for equity options the market capacity is given depending on the time-to-expiry and the (modified) moneyness of the option.

The market capacity can for instance be measured by the daily average trading volume measured by the number of contracts traded.

3.5.2 Aggregation of the Liquidity Risk Components for a Liquidation Group Split In case of a liquidation, heuristic hedging approaches will be implemented to reflect the liquidity- related portfolio composition. As a consequence, diversification is granted to some extent in terms of the diversification of market risk. Such diversification effects are captured using a diversification factor α, which is used to reduce the overall liquidity premium of the portfolio to a level reflecting the actually utilized liquidation procedure.

24. The modified moneyness is defined as: Ž‘‰ሺܵൗሻ ݉݊ ൌ ܭ ξݐ Where: - S is the current price of the underlying - K is the strike price of the option - T is the time to expiry 25. Short positions are indicated by negative position sizes.

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In order to aggregate the liquidity risk components for all positions i within a given liquidation group split l the following formula is used:

௣௢௦ ܮܥ௞ ൌߙ෍หܮܥ௜ ห ௟א௜

The factor α will be determined based on the level of market risk diversification within a liquidation group split. For a well diversified long-short portfolio the factor is smaller than for portfolios consisting mainly of highly correlated, directional positions.

The market risk diversification will be quantified through the ratio of the market risk for the whole liquidation group split l (VaRl) and the sum of the market risk figures measured on position 26 ௣௢௦ ௟ ܸܴܽ௜ ). While the portfolio VaR takes diversificationאlevel for this liquidation group (σ௜ effects into account, the sum of the positional VaR figures does not.

The aggregated market risk figure for liquidation group split l is calculated using the following formula27: ݉݁ܽ݊ ܸܴܽ ൌ ൛ܸܴܽ௛௜௦௧ൟ ௟ ܽ߳ܣ ௟ǡ௔ where:

௛௜௦௧  ܸܴܽ௟ǡ௔ is the market risk measure for the filtered historical scenarios of liquidation group split l for subsample a. The aggregation function is a parameter provided by Eurex Clearing.

Furthermore an additional floor αfloor will be applied in order to assure a minimum liquidity risk component even for well-diversified portfolios28.

ܸܴܽ௟ ߙ ൌ ƒšሼ ௣௢௦ ǡߙ௙௟௢௢௥ሽ ௟ ܸܴܽ௜אσ௜

26. The position VaR figures are calculated by multiplying the instrument VaR figures (AIVAR) provided by Eurex Clearing with the absolute value of the number of contracts for each instrument. For each instrument two figures are delivered, one to be used for long positions and one for short positions, since returns for nonlinear instruments are not symmet- rically distributed. 27. The risk measure specification used for the calculation of the diversification factor might differ from the risk measure used for the calculation of the market risk component (e.g. usually the diversification factor will be calculated on a lower quantile than the risk measure used to calculate the market risk component). All risk measure specifications including the method to aggregate the scenario subsamples will be provided by Eurex Clearing. The market risk mea- sure is not calculated based on stressed periods. 28. The floor value for the diversification factor will be provided by Eurex Clearing via the transparency enabler files. The diversification factor is capped by 1.

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Example - Calculation of Liquidity Risk Component:

In the following lookup table, exemplary liquidity factors depending on the position size relative to the market capacity are illustrated for the asset classes of the representative instruments. The market capacities are provided by Eurex Clearing. Relative Market Equity Futures Equity Derivatives Bond Futures Size (Large Cap) (Options) 5% 0.05 0.05 0.05 10%0.250.250.25 15% 0.5 0.5 0.5 20%0.750.750.75 40% 0.75 0.75 0.75 60%0.750.750.75 100% 0.75 0.75 0.75 >100% 0.75 0.75 0.75

Table 14: Liquidity Factors

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The liquidity factors are used to calculate the liquidity risk component of every position along with the market risk measure. Instrument DAX Option DAX Future BOBL Future CONF Future Option Positional Aggregated Market 4,810.79 4,853.25 708.28 15,600.54 Risk Measure MRi Relative Position Size: 0.10% 0.05% 0.03% 0.10% Position Size / Market Capacity Liquidity Factor1 0.0010 0.0005 0.0003 0.0010 Liquidity Premium [bps]2 100.00 10 100 15 Position Size * TUV 25 1 50 1 (Number of contracts) Net gross Ratio ngr3 1/1=100% 1/1=100% 1/1=100% 1/1=100% Current Price [EUR] 1,487.00 146,925.00 2,223.34 136,188.89 Position Value 100%*1*25* 146,925.00 111,166.80 136,188.89 1487,00 =37,175.00 Position-wise Liquidity Risk 4810.79*0.0 149.35 1,111.90 219.88 Component 010+100/ 10,000*3717 5.00=376.56

1.Values were taken from the lookup table. 2.The bid-ask spreads are provided by Eurex Clearing for every product type, time-to-expiry bucket and - in case of options - moneyness bucket. The illustrated values from the example were chosen for didactic reasons and do not necessarily represent realistic bid-ask spreads. 3.The net gross ratio is equal to one as all instruments are in a separate risk bucket.

Table 15 Example - Calculation of Liquidity Risk Component by Position

For the aggregation of liquidity risk components the alpha factor needs to be calculated using the positional market risk measures and the diversified market risk measure for the complete portfolio. Liquidation Group Diversified VaR Sum of aggregated Alpha Alpha Factor Split market risk measures Floor1 for all components of liquidation group split 1, non-expiring 6,184.99 6,184.99 Max(10%;6,184.99 /6,184.99) =100% 30% 1, expiring 6,239.58 6,239.58 100% 2, non-expiring 19,109.56 5,123.49 92% +15,615.12

1.In the given example the floor is set to 10%. This value was only chosen for didactic reasons.

Table 16 Example - Calculation of alpha factors for each Liquidation Group Split

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This leads to the following liquidity risk components for the different liquidation group splits: Liquidation Group Sum of absolute Liquidity Alpha Factor Liquidity Risk Components Split Risk Components Liquidation Group Split 1, non-expiring 376.56 100% 376.56*1.00=376.56 1, expiring 149.35 100% 149.35*1.00=149.35 1, non-expiring 1,111.90+219.88 92% (1,111.90+219.88)*0.92 =1,331.78 =1,227.15

Table 17 Example - Calculation of Liquidity Risk Component for Liquidation Group Splits

3.6 Putting all Components Together The total initial margin component for a liquidation group consists of the aggregated market risk components over all scenario subsamples including the respective model adjustments and liquidation group specific liquidity risk components29.

The VaR figures for each subsample of the filtered historical and the stressed scenarios are aggregated by taking the mean VaR figures of the subsamples separately for the filtered historical and the stressed VaR including the relevant model adjustments.

The resulting two VaR figures for the stressed and the filtered historical scenarios need to be aggregated as well. This is done by taking the maximum of the filtered historical VaR and a 30 scaled stressed VaR using a configurable scaling factor with default value ws=0.70. The

scaling factor wh for the historical scenarios is set to 1. Both scaling factors are provided by Eurex Clearing.

In conclusion this leads to the following formula for the total initial margin for a liquidation group split l:

݉݁ܽ݊ ௛௜௦௧ ௛௜௦௧ ݉݁ܽ݊ ௦௧௥௘௦௦௘ௗ ௦௧௥௘௦௦௘ௗ ௟ܥܮ ௟ǡ௔ ൟሽ ൅ܧܥ௟ǡ௔ ൟǡݓ௦ ൛ܸܴܽ௟ǡ௔ ൅ܧܥ௟ǡ௔ ൅ܤܥ௟ ൌƒšሼݓ௛ ൛ܸܴܽ௟ǡ௔ ൅ܯܫ ܽ߳ܣ௛ ܽ߳ܣ௦

29. If risk measures for additional scenario types beyond the historical and stressed scenarios are calculated those risk measures will be aggregated using the specified method as well. 30. The confidence levels of the VaR figures are set to 99% in accordance to Eurex Clearing's policy. By taking into account only the scenarios from the most stressful periods the stressed VaR is actually based on a confidence level higher than 99% (e.g. approximately 5% of the all historical data is marked as a “stress period” in this context). To account for this, the risk figure from the stress period is scaled down. Other scenario types might be introduced, too. For these other scenario types a scaling factor can be applied as well. All scaling factors will be provided by Eurex Clearing via the input files as well.

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 IMl is the total initial margin for liquidation group split l

 Ah is the set of scenarios subsamples based on the Historical Simulation

 As is the set of stressed scenarios subsamples

௛௜௦௧  ܸܴܽ௟ǡ௔ is the n-day VaR based on the Historical Simulation for liquidation group split l for the a-th scenario subsample.

௛௜௦௧  ܥܤ௟ǡ௔ is the correlation break adjustment based on the Historical Simulation for liquidation group split l for the a-th scenario subsample.

௛௜௦௧  ܥܧ௟ǡ௔ is the n-day compression error based on the Historical Simulation for liquidation group split l for the a-th scenario subsample.

௦௧௥௘௦௦௘ௗ  ܸܴܽ௟ǡ௔ is the n-day VaR based on the stressed scenarios for the a-th scenario subsam- ple.

௦௧௥௘௦௦௘ௗ  ܥܧ௟ǡ௔ is the n-day compression error for liquidation group split l based on the stressed scenarios for the a-th scenario subsample.

 LCl is the liquidity risk component for liquidation group split l

 wh and ws are aforementioned scaling factors provided by Eurex Clearing

The methods to aggregate the historical and stressed risk measures as well as the subsample risk measures are configurable parameters and will be provided by Eurex Clearing via the transparency enabler files31.

The initial margin figures for several liquidation group splits are added to obtain initial margin figures on higher levels of the portfolio hierarchy structure such as the initial margin on account level.

31. The possible aggregation methods comprise: mean, weighted mean, median and maximum.

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Example - Putting all components together:

The initial margin is calculated using the tail risk measures and the model adjustments calculated in sections 3.3.4 and 3.4. Liquidation Group 1, non-expiring Liquidation Group 1, expiring Figure Scenario Scenario Scenario Scenario Subsample 1 Subsample 2 Subsample 1 Subsample 2 VaR (FHS1) 16,197.31 14,141.75 14,776.66 13,306.43 + Correlation Break 1,849.35 251.43 1,194.77 856.89 Adjustment + Compression Error 446.10 594.80 0.00 0.00 Adjustment

hist 18,492.76 14,987.99 15,971.43 14,163.32 VaRa,ModelError

VaR (Stressed) 31,192.36 23,764.93 20,867.16 22,760.19 + Compression Error 297.40 520.45 0 0 Adjustment

Scaling Factor ws 0.7

stressed 22,042.83 16,999.77 14,607.01 15,932.13 VaRa,ModelError  ws

1.Filtered Historical Simulation

Table 18 Example - Putting all components together LG1

Liquidation Group 2, non-expiring Figure Scenario Scenario Subsample 1 Subsample 2 VaR (FHS) 42,690.28 54,173.14 + Correlation Break 2,510.66 2,056.50 Adjustment + Compression Error 9.09 14.78 Adjustment

hist 45,210.03 56,244.43 VaRa,ModelError

VaR (Stressed) 58,893.33 61,910.91 + Compression Error 9.89 32.68 Adjustment

Scaling Factor w1 0.7

stressed 41,232.26 43,360.51 VaRa,ModelError  ws

Table 19 Example - Putting all components together LG 2, Non-expiring

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The initial margin for both liquidation groups is calculated taking into account the total market risk components aggregated over the filtered historical and stressed VaR and the liquidity risk component as calculated in section 3.5. LG 1 LG 1 LG 2 non-expiring expiring non-expiring Aggregated =max(mean(18,492.76; 15,269.57 50,727.23 Market Risk 14,987.99); mean(22,042.83; Component 16,999.77))=19,521.30 Liquidity Risk 376.56 149.35 1,227.15 Component Total Initial 19,897.86 15,418.92 51,954.37 Margin

Table 20 Example - Calculation of Initial Margins

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4 Additional Explanations & Special Cases

4.1 Special Treatment of Interest Rate Swaps Interest rate swaps (IRS) are treated differently from other instruments due to product specific requirements and conventions. Details concerning the methods used for the treatment of interest rate swaps will be described in a separate document (see [5] in appendix 6.1) while the document at hand only briefly mentions the main differences:

Particularly the following points differ from the methods described in the previous sections:

 For the replication of margin requirements, the simulated yield curves are provided to custom- ers. In order to replicate margin calculations, additional information such as the utilized day count conventions and interpolation methods will be delivered.

 The liquidity risk component for interest rate swaps will be calculated using a modified approach. The adjustment will be calculated on portfolio level by construction of a suitable hedge portfolio consisting of artificial swaps based on bucket sensitivities of the correspond- ing portfolios.

4.2 Treatment of Foreign Currency Risk For instruments denominated in a different currency than the clearing currency an additional risk factor in form of the spot rate between the foreign currency and clearing currency will have to be taken into account.

In case all possible instruments of a liquidation group are denominated in the same currency, the initial margin will be calculated in this product currency according to the methods described in the previous sections. Otherwise the initial margin will be calculated in the clearing currency chosen by the clearing member. Therefore, the currency of the calculated initial margin figure be calculated will always be defined based on the liquidation group composition. This currency is called a liquidation group’s target currency.

It should be noted that the currency in which the initial margin figure is calculated does not depend on the actual subportfolio composition of a clearing member, but only on the global definition of the liquidation group. Therefore, even in case a clearing member’s positions are all denominated in the same currency, the target currency of the initial margin might still be the member’s clearing currency as the liquidation group in general consists of instruments denominated in different currencies.

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In that case the profit and loss distributions will be calculated in the clearing currency. The scenario prices and the current price both given in product currency are converted to the clearing currency using the foreign exchange rate scenarios and the current foreign exchange rate. The calculation of the initial margin figures can then be conducted according to the methods described in the previous sections based on the converted profit and loss distribution and leads to an initial margin in the clearing currency of the respective portfolio.

In case collateral will be delivered in a currency other than the clearing currency, hair cuts according to the RBM methodology will be applied when converting the collateral into the clearing currency32.

Example

The following simplified examples illustrate the necessary FX conversions. The following table shows the liquidation group composition for two exemplary liquidation groups each consisting only of two instruments. Instrument Liquidation Group Product Currency DAX Option LG 1 EUR DAX Future LG 1 EUR Bobl-Future Option LG 2 EUR Gilt Future LG 2 GBP

Table 21 Example - Sample Instruments, Product Currencies and Liquidation Group Composition

Furthermore, in this example the following clearing members are given. Clearing Clearing Position in DAX Position in DAX Position in Position in Gilt Member Currency Option Future Bobl-Future Future Option A EUR 1 1 1 0 BCHF1101 C EUR 1 1 1 1 DCHF1111

Table 22 Example - Clearing Members and their Positions

As liquidation group 1 contains only instruments denominated in EUR, its target currency is EUR and the initial margin figures for this liquidation group will always be calculated in EUR. Liquidation Group 2 contains instruments in EUR and GBP and therefore the margin will always

32. As an exception, if all instruments in a liquidation group are denominated in the same currency other than the clearing currency and the initial margin is subsequently calculated in the unique product currency. Any collateral posted in this product currency will be taken into account before the haircuts will be applied.

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be calculated in the clearing currency of the respective member even if the clearing member B only holds positions denominated in GBP. Clearing Initial Margin LG 1 Initial Margin LG 2 Member A Calculated in product currency EUR: Calculated in clearing currency EUR: No currency conversion necessary No currency conversion necessary BCalculated in product currency EUR: Calculated in clearing currency CHF: No currency conversion necessary P&L of Gilt future is converted to CHF C Calculated in product currency EUR: Calculated in clearing currency EUR: No currency conversion necessary P&L of Gilt future is converted to EUR DCalculated in product currency EUR: Calculated in clearing currency CHF: No currency conversion necessary P&L of Bobl Future Option and of the Gilt Future is converted to CHF

Table 23 Example - Necessary currency conversions in the example

4.3 Special Treatment of Instruments Close to Expiry Instrument that expire within the pre-defined holding period are treated separately in the default management process from the other instruments of a liquidation group. For example, those positions are either closed immediately or they are hedged separately from the non-expiring positions.

Due to the separate treatment of the expiring positions, no margin offsets are granted between those instruments and the instruments with a longer time to expiry. Therefore two liquidation group splits are derived from the liquidation group containing the longer dated instruments and the expiring instruments33. Margin offsets are granted within the liquidation group splits, but will not be granted between those splits.

33. Eurex Clearing will map the instruments to liquidation group splits and provide this information via the transparency enabler files.

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5 Margin Replication

To facilitate transparency Eurex Clearing enables its members to verify and reproduce the calculation of initial margins. Therefore Eurex Clearing provides detailed information in form of several structured files - hence called transparency enabler files - to its clearing members.

The initial margins for each liquidation group can be replicated by the clearing members themselves outside Eurex Clearing’s systems as Eurex Clearing provides all necessary input parameters as well as the methodological documentation necessary for the calculation of the margin amounts.

The following figure schematically illustrates the margin replication.

Information provided by Eurex Clearing to CM CM internal information Theoretical prices & Liquidity configuration Aggregation Rules additional info … tables Portfolio structure

• … Position 1 Theoretical prices • • Scenario groups (for Market Liquidity Position 2 Compression errors … • market risk) capacity factor

Instrument descriptions Position n

Replication outside Eurex Clearing

Market risk component Compression error Liquidity risk incl. correlation break adjustment component adjustment

Figure 6: Margin Replication and Information provided by Eurex Clearing

5.1 Information Provided by Eurex Clearing All transparency enabler files are given in a machine-readable structure which allows for automated processing.

The files contain the following information34:

 theoretical prices under all scenarios and instrument descriptions in product currency

 risk measure details

 market risk aggregation rules

 market capacities

 liquidity factors

 FX rates

34. For interest rate swaps different input files will be provided, which will be explained in a subsequent document. More information concerning interest rate swaps can be obtained in [5].

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The following sections describe the files delivered by Eurex Clearing. A technical description of the input files can be found in section 5.3.

5.1.1 Overview File Structure The following graphic illustrates the interdependencies of the transparency enabler files in the process to calculate the initial margin figures.

FX Rates Theoretical Market Market Risk Risk Measure Configuration Prices & Inst. Liquidity Capacity Aggregation Configuration Configuration Factors Config Configuration Configuration

VaR Figures

Stressed Filtered Period Historical Correlation Break Simulation Compression Error Adjustment Adjustment

Market Risk Component Liquidity Risk Component

Initial Margin

Figure 7: Overview File Structure

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The following tables summarizes the relationships between the tables and components of the initial margin figure: File Utilizations

Theoretical Prices & Instrument  Calculation of VaR figures for market risk component Description  Compression errors

 Correlation break adjustment

 Liquidity risk component

Market Risk Aggregation  Aggregation of VaR figures for market risk component Configuration  Aggregation of VaR figures for liquidity risk component

 Aggregation of the market risk component

Risk Measure Configuration  Calculation of VaR figures for market risk component

 Calculation of VaR figures for liquidity risk component

 Calculation of correlation break adjustment

FX Rates Configuration  Calculation of VaR figures for market risk component

 Calculation of VaR figures for liquidity risk component

 Calculation of correlation break adjustment

Market Capacity Configuration  Liquidity risk component

Liquidity Factor Configuration  Liquidity risk component

Table 24: Overview Files

5.1.2 Theoretical Prices and Instrument Configuration The file “Theoretical_Prices_and_Instrument_Configuration” contains prices of all instruments for the scenarios based on the Historical Simulation and the stressed scenarios35. All prices reflect hypothetical returns over the n-day holding period of the respective liquidation group.

The prices are used to calculate the profit and loss distributions36, which are the basis for the subsequent estimation of risk measures for the margin components.

In addition to their prices, structured descriptions of the instruments are provided containing additional information such as the product and asset types.

For options further asset-type specific data is included such as the moneyness, Vega and current implied volatility. Additionally, compression errors and VaR figures on instrument level are delivered for all scenarios in product currency and the two clearing currencies EUR and CHF37.

35. Compare to section 3.3.1 (historical scenarios) and 3.3.2 (stressed scenarios). The number of historical and stressed scenario prices is flexible. Further types of scenario prices may be added in the future. 36. Compare to section 3.3.3

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The mapping of instruments to distinct liquidation groups and sets of FX rates can also be extracted from this file.

5.1.3 Risk Measure Configuration The “Risk_Measure_Configuration” file contains the detailed specifications of the risk measures used for the margin calculation. The risk measures are specified on liquidation group level. All values are configurable parameters and can be changed at the discretion of Eurex Clearing. The risk measure specification is given as for each liquidation group.

 utilized risk measure

 confidence level

 robustness enhancement, i.e. utilization of the robust VaR methodology

 scaling factor utilized in robustness enhancement

 flag indicating the risk measure type (e.g. filtered historical or stressed)

 flag indicating if correlation break adjustment will be calculated for this risk measure

 specification for correlation break adjustment (time-window size, cap, floor and kappa κ fac- tor)

 flag indicating if liquidity risk component will be calculated based on this risk measure

 specification of liquidity risk component

5.1.4 Market Risk Aggregation Configuration This file “Market_Risk_Aggregation_Configuration” contains the description for the aggregation of the tail risk measures for each liquidation group including the aggregation of the subsamples38. Scaling factors for the VaR figures for each risk measure are given and the aggregation function, i.e. minimum, maximum, average or median will be provided for each liquidation group.

5.1.5 Market Capacities Configuration The lookup tables for the market capacities of the different product types are defined in file “Market_Capacities_Configuration” as described in section 3.5. The dimensions of the lookup tables are dependent on the corresponding product type. Furthermore, the liquidity premiums are

37. Further clearing currencies may be introduced in the future. 38. In case additional scenario types beyond the historical and stressed are introduced by Eurex Clearing in the future, the file will also include the aggregation methods for those scenario types.

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given in basispoints for each product type, expiry bucket and, in case of options, modified moneyness buckets.

5.1.6 Liquidity Factors Configuration The lookup tables for the liquidity factors are provided depending on the size of a position relative to the market capacity for every liquidity class in file “Liquidity_Factors_Configuration”. Each instrument is assigned to a liquidity class. The liquidity factor value will be interpolated linearly between the upper and lower bound liquidity factors for a given relative market size of a position39.

5.1.7 Foreign Exchange Rates Configuration In order to convert instruments denominated in a foreign currency to the clearing currency several sets of foreign exchange rates are provided by Eurex Clearing in the file “Foreign_Exchange_Rates_Configuration”. Each set of FX rates comprises FX rates for every risk measure (e.g. filtered historical and stressed) and the current FX rate. Every set of FX rates is tagged by a unique identifier, which can also be found in the theoretical price and instrument description file. The file contains all foreign exchange rates pairs, for all combinations of products currency and clearing currency.

5.2 Replication of the Margin Calculation outside Eurex Clearing Given the files containing the parameters for the calculation of the initial margin, the clearing members can replicate the margin payments for their liquidation groups based on the positions of their portfolio according to the methods described in chapter 3.

The ability to replicate the margins facilitates transparency and the acceptance of the margin amounts and the utilized methodology.

An algorithmic description of the initial margin calculation in accordance with the exemplary calculations in the spreadsheet [4] can be found in section 5.3.6.

The level of precision for the margin calculation is explained in section 6.3

5.3 Input File Format for Margin Replication The following section gives a technical overview over the input files that can be used to replicate the margin amounts and includes exemplary input files. The file formats given below are still subject to change at the discretion of Eurex Clearing. The files will be provided as csv-styled text

39. Compare to section 6.4.

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files of flexible length. Each file consists of several sections, which contain different types of fields. Semicolons are used as separators between two values within one line. Between two lines a windows-style line separator will be used. For all numerical values the digits after the decimal points are illustrated. If necessary, all values will be rounded to that precision. All files should end with an End of file information. The format of the same is described in section 5.3.7.

5.3.1 “Theoretical_Prices_and_Instrument_Configuration” File The following table contains the field names, the data types and exemplary values for the theoretical prices and instruments files40. The compression errors, instrument VaR values additional instrument VaR figures can be provided for a variable number of currencies. These currencies should comprise at least the clearing currencies and the product currency. The number of historical and stressed scenario prices is flexible.

The FX rate set can be used to identify the FX rates given in the FX rates configuration file to be used in case of a necessary currency conversion. In addition to historical and stressed scenario prices further scenario types may be introduced at a later time. Unless specifically stated, all price information is given in product currency.

5.3.1.1 General File Structure

The theoretical price file is structured according to the following rules.

Section P: For all products

Section E: For all expirations of the current product

Section S for all series associated with an expiry date

Section FX: FX rate set for the series

Section N: Neutral Scenario (Current Price) of the current series

Section RMS for all risk measures set associated with a series

Section LH: Holding period for risk measure set

Section SP Scenario prices for risk measure set,

Sections CE Compression errors for the risk measure set

Next risk measure set

40. Due to the additional information provided by Eurex Clearing the “Theoretical_Prices_and_Instrument_Configuration” file size can be substantially larger than the old theoretical price file used in the RBM calculations.

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Sections IVAR and AIVAR: Instrument VaRs and additional instrument VaRs in respective currencies for the series and for longs and shorts  respectively:

Next series

Next expiration

Next Product

5.3.1.2 Fields

The input files contain the following fields:

Section Field name Value type1 Value example Remark Product P Product ID String (4) ODAX Tick Size Number (4) 0.1000 Tick size of the product Tick Value Number (4) 0.5000 Tick value of the product Currency String (3) EUR Product currency Liquidity Class String (24) EOLC The liquidity class will be used to calculate the liquidity adjustment. Each instrument will be assigned to a liquidity class. Example: “EOLC” as abbreviation for “Equity options (large cap)”2 Liquidation String (30) LG1 Liquidation group to which the Group product is assigned to Margin Style String (1) F Margin style: F - Futures style T - Traditional Expiration E Expiration Year Number (0) 11 11=2011, 12=2012, … Expiration Number (0) 12 1 - January, 2 - February, … Month Expiration Day Number (0) 15 Calendar day of expiration, provided for standard and flexible instruments Days to expiry Number (0) 30 in business days, for options theoretical pricing calendar days Series S Call Put Flag String (1) C C - call, P - put, empty for futures, Exercise Price Number (6) 7700.000000 Exercise price of an option, zero for futures

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Section Field name Value type1 Value example Remark Series Version Number (0) 1 This field contains the version Number number assigned to the series at creation. The value is zero for all standard series not changed as a result of capital adjustment to the underlying instrument and for futures contracts. Valid values include: 0 - standard series version or futures contract 1 - adjusted series version from most recent capital adjustment 2 - adjusted series version from the second most recent capital adjustment 3 - adjusted series version from the third most recent capital adjustment Time-To-Expiry String (20) ODAX_C_3 Compare to table Bucket ID “TTE_Bucket_Information”, used for the calculation of the liquidity adjustment Moneyness String (20) ODAX_C_1 Empty for futures, compare to table Bucket ID “Moneyness_Bucket_Information”, used for the calculation of the liquidity component Risk Bucket String (20) ODAX_C_3_1 The risk buckets are utilized in the calculation of the liquidity adjustment as the effective net gross ratio is calculated for each risk bucket, each instrument will be assigned to a risk bucket3 Series Status String (1) A Series status: Active: A Expired: E Trading Unit Number (4) 5.0000 This field contains the quantity of the underlying instrument traded per contract. Liquidation String (30) LG1_nexp The identifier for the liquidation Group Split group splits consists of the identifier for the liquidation group and an additional suffix indicating if the position is expiring or not.

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Section Field name Value type1 Value example Remark Option Vega Number (6) 5.000000 Vega divided by 100 represents the amount that an option contract's value changes in reaction to a 1 percent absolute shift in the volatility (measured in percent) of the underlying, zero for futures Implied Number (4) 20.0000 Implied volatility used for the Volatility calculation of the neutral scenario price, annualized volatility in percent, zero for futures Interest Rate Number (6) 3.123456 This fields contains the security risk free interest rate used (continuous compounding). This value is shown in percent. Flex Product ID String (4) This field contains the ID of the product for which flexible series were created. This field is only filled for flexible products and empty for standard products. Settlement type String (1) C Settlement type of the contract as delivered by Eurex. Current list of settlement types are: C - Cash Settlement E - Physical Settlement D - Derivative N - Notional Settlement P - Payment-versus-Payment S - Stock T - Cascade A - Alternate Series exercise String(1) E Defines the exercise style style flag A - American E - European Empty for Futures Flex Series Flag String (1) N Contract is a flex contract Y- Yes N - No FX FX Set String (10) FX1 Set of FX scenarios used for this instrument, compare to exchange rate file, each series is assigned to a unique risk measure set

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Section Field name Value type1 Value example Remark Neutral Theoretical Number (6) 7650.000000 Current price of the series also Scenario N price for neutral denoted as neutral scenario scenario RMS Risk Measure String (30) RMS1 Several risk measure sets can Set exists for every series LH Liquidation Number (0) 5 Holding Period (=liquidation Horizon (= horizon) used for the historical Holding Period) scenarios, in business days Historical Scenarios SP Scenarios Prices Number (6) 7645.500000 The first scenario price is associated with the first scenario, the second price to the second scenario and so on. The first scenario price is also assigned to the first scenario subsample, the second to the second scenario subsample and so on. CE Compression Number (6) 10.000000 LH (=holding period) compression error errors for one contract Currency String (3) EUR Currency for the compression error IVAR Instrument VaR Number (6) 400.250000 VaR figure on instrument level used to calculate the position-wise liquidity component for a position size of 1, both for longs and shorts Long short String (1) L Indicates whether the IVAR is valid Indicator for long or short positions. Currency String (3) EUR Currency for the instrument VaR AIVAR Additional Number (6) 400.250000 Additional VaR figure on Instrument VaR instrument level. The additional instrument VaR will be used to calculate the diversification factor of the liquidity adjustment for a position size of 1, both for longs and shorts. Long short String (1) L Indicates whether the AIVAR is Indicator valid for long or short positions. Currency String (3) EUR Currency for the additional instrument VaR

1.The number in the bracket indicates how many digits after the decimal point are provided for numbers and the maximum length of the field for String fields. 2.The abbreviation for the liquidity classes, time-to-expiry buckets and moneyness buckets are explained in additional files, which will not be needed for the replication of the initial margin, but will be provided by Eurex Clearing for informative purposes. These files will be described in section 6.6. The liquidity class information will be utilized to calculate the liquidity adjustment as the liquidity factors are given for each liquidity class.

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3.Compare to specification for the calculation of the liquidity component The file should end with an End of file information. The format of the same is described in section 5.3.7.

5.3.1.3 Examples

The structure of an exemplary input file for a non-flex product is given as:

IVAR and AIVAR are computed at the instrument level for a position size of 1, both for longs and shorts. The P&L vectors of historical scenarios are only used to compute the IVAR and AIVAR. The P&L vectors from the stressed RMS are not taken into account for the liquidity add-on.

P;OFTE;2.0000;1.0000;EUR;EOLC;LG17;T E;11;12;0;30 S;C;7700.000000;1;OFTE_P_1;OFTE_P_1;OFTE_P_1_1;A;5.0000;LG1_nexp;5.000000;20.0000;3.1234 56;;C;E;N FX;FX1 N;7650.000000 RMS;RMS1 LH;5 SP;750;7645.100000;7532.000000;7700.520000;7650.503000;… CE;10.123456;…;15.123456;EUR CE;11.123456;…;16.123456;CHF RMS;RMS2 LH;5 SP;7645.100000;7532.000000;7700.520000;7650.503000;… CE;10.123456;…;15.123456;EUR CE;11.123456;…;16.123456;CHF IVAR;100.111111;L;EUR IVAR;100.111000;S;EUR IVAR;200.222222;L;CHF IVAR;200.222000;S;CHF AIVAR;150.111111;L;EUR AIVAR;150.111111;S;EUR AIVAR;300.222222;L;CHF AIVAR;300.222222;S;CHF

*EOF*;P;99999999;20120523;PRGCA;PRGCA;OI;THEORETICAL PRICES AND INSTRUMENT CONFIG

5.3.2 “Risk_Measure_Configuration” File The risk measure configuration file will be provided by Eurex Clearing on liquidation group level enabling a separate risk measure specification for each liquidation group. The risk measures are specified at least for the historical and the stressed scenarios. Other risk measures might be added over time.

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5.3.2.1 General File Structure

Section LGS: For every liquidation group

Section RMS: For every risk measure set

Risk measure specifications

Next risk measure set

Next liquidation group

5.3.2.2 Fields

The file contains the following fields: Section Field name Value type Value example Remark Liquidation Liquidation String (30) LG1 Defines for which liquidation group Group Group the following specification is valid Identifier LG Currency type String (1) C Provides the information whether Flag the clearing currency is used or product currency for computing the initial margin in this liquidation group. C - Clearing currency, when products with different currencies make up the liquidation group. P - Product currency, when products with the same currency make up the liquidation group. Risk Risk Measure String (30) RMS1 Risk measure set identifier Measure Set ID RMS Historical / String (1) H Risk measure is used for: Stressed H - historical scenarios F - filtered historical scenarios S - stressed scenarios Risk Measure String (1) V Utilized risk measure: V - VaR C - CVaR U - undiversified VaR Confidence Number (5) 95.00000 Confidence level for risk measure Level before scaling, in percent Robustness String (1) Y Use robustness enhancement for this risk measure Y - Yes N - No

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Section Field name Value type Value example Remark Scaling Factor Number (5) 1.92123 Scaling factor for robustness enhancement 1 if robustness enhancement is not used (Robustness - N) Correlation String (1) Y Will correlation break adjustment Break Yes / No be added to risk measure Y - Yes N - No Moving sub- Number (0) 60 Size of the sub-windows used for window the calculation of the correlation break expressed as number of scenarios. Empty if correlation break is not used for current risk measure set. Confidence Number (5) 95.00123 Confidence level used for the Level calculation of the correlation break, empty if correlation break adjustment is not used, in percent Cap Number (5) 20.00001 In percent, maximum correlation break adjustment in percent of market risk, empty if correlation break adjustment is not used Floor Number (5) 10.00001 In percent, minimum correlation break adjustment in percent of market risk, empty if correlation break adjustment is not used Multiplier Number (5) 1.12345 Multiplier for the calculation of the correlation break adjustment Liquidity String (1) Y Will liquidity component be applied Component to the risk measure: Y / N Y - Yes N - No Confidence Number (5) 90.00123 Confidence level for the calculation Level of the diversification factor alpha, Diversification Empty if liquidity component is not Factor used Alpha Floor Number (5) 10.00000 Floor for diversification factor used for the calculation of the liquidity component in percent Empty if liquidity adjustment is not used The file should end with a End of file information. The format of the same is described in section 5.3.7.

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5.3.2.3 Example

An exemplary file will have the following structure:

LG;LG1 RMS;RMS1;H;V;95.12345;Y;1.92123;Y;60;90.00123;20.00001;10.00001;1.00000;Y;90.00123;10.12 345 RMS;RMS2;S;V;95.12345;Y;1.92345;N;;;;;N;; … *EOF*;P;2;20120523;EUREX;EUREX;NI;RISK MEASURE CONFIG

5.3.3 “Market_Risk_Aggregation_Configuration” File The aggregation rules for the market risk measures are specified independently on liquidation group level enabling a separate specification of the aggregation rules for every liquidation group. Both the aggregation of the different scenario types (e.g. historical scenarios and stressed scenarios) and the aggregation of the scenario subsamples are described in this file. The market risk aggregation file contains the following data fields:

5.3.3.1 General File Structure

Section LGS: For every liquidation group

Section RM: one risk method for each liquidation group

Aggregation method for risk measure set of the risk method

Section RMS: For every risk measure set

Subsample Aggregation Method

Weighting factor of risk measure set

Next risk measure set

End risk method

Next liquidation group

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5.3.3.2 Fields

The following fields are contained within the file: Section Field name Value type Value example Remark Liquidation Liquidation String (30) LG1 Defines for which liquidation group Group Group the following risk method Identifier LG specification is valid RM Risk Method ID String (30) RM1 Risk method ID The risk method defines the aggregation concerning risk measure sets Aggregation String (10) Max Aggregation method to aggregate Method the different risk measures for each risk method Max / Avg / Sum / Med (maximum / average / sum / median / minimum) RMS Risk Measure String (30) RMS1 Risk measure set of a given risk Set ID method, compare to risk measure configuration file Weighting factor Number (5) 70.000000 Weighting factor for the aggregated risk measure in percent Aggregation String (10) Max Subsample aggregation method Method Max / Avg / Sum / Med (maximum / average / sum / median)

The file should end with a End of file information. The format of the same is described in section 5.3.7.

5.3.3.3 Example

An exemplary file will have the following structure:

LG;LG1 RM;RM1;Max RMS;RMS1;100.00000;Median RMS;RMS2;70.12345;Median LG;LG2 RM;RM1;Median RMS;RMS1;100.00000;Median RMS;RMS2;70.12345;Median

*EOF*;P;2;20120523;EUREX;EUREX;NI;RISK MEASURE AGGREGATION CONFIG

5.3.4 “Market_Capacities_Configuration” File The market capacities file provides information concerning the market capacities and liquidity premiums for the positions.

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5.3.4.1 Fields

The market capacities file contains the following data fields. The market capacities and liquidity premiums are used for the calculation of the liquidity component. Section Field name Value type Value example Remark Product Line String (1) O O - Option F - Future Other product lines might be introduced at a later time Product ID String (4) ODAX U/L_ISIN String (12) ISIN of underlying Put Call Flag String (1) P P - Put C- Call Empty for futures Time-To-Expiry String (20) ODAX_P_1 Compare to table Bucket ID “TTE_Bucket_Information” Moneyness String (20) ODAX_P_1 Empty for futures, compare to Bucket ID “Moneyness_Bucket_Information” table Market Capacity Number (5) 600.00000 Derived from trading volume or similar figure Liquidity Number (5) 200.00000 The liquidity premium will be used Premium for the calculation of the liquidity component1 given in bps 1.The liquidity premium is given as ȁ௕௜ௗ೔ି௔௦௞೔ȁ ȁ௕௜ௗ೔ା௔௦௞೔ȁ The file should end with a End of file information. The format of the same is described in section 5.3.7.

5.3.4.2 Example

An exemplary file will have the following structure:

O;ODAX;DE0009652644;C;ODAX_C_1;ODAX_C_1;10.00000;100.00000 O;ODAX;DE0009652644;C;ODAX_C_2;ODAX_C_1;100.00000;50.00000 O;ODAX;DE0009652644;C;ODAX_C_3;ODAX_C_1;90.00000;80.00000 O;ODAX;DE0009652644;C;ODAX_C_3;ODAX_C_2;100.00000;90.00000 … O;OFBD;DE0009652644;P;OFBD_P_1;OFBD_P_1;30.00000;80.00000 O;OFBD;DE0009652644;P;OFBD_P_2;OFBD_P_1;40.00000;70.00000 O;OFBD;DE0009652644;P;OFBD_P_3;OFBD_P_1;50.00000;60.00000 … F;ALFV;DE0009652644;;ALFV_1;;20.00000;100.00000 F;ALFV;DE0009652644;;ALFV_2;;10.00000;120.00000 F;ALVF;DE0009652644;;ALFV_3;;30.00000;130.00000 … F;FBND;DE0009652651;;FBND_1;;30.00000;140.00000 … *EOF*;P;9999;20120523;EUREX;EUREX;NI;MARKET CAPACITIES CONFIG

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5.3.5 “Liquidity_Factors_Configuration” File The liquidity factors are used for the calculation of the liquidity risk component. Each instrument is assigned to a liquidity class. The liquidity factor is determined based on the net effective position size of the position.

5.3.5.1 Fields

Section Field name Value type Value example Remark Liquidity String (24) EOLC EOLC = “Equity Option Large Cap” Class Minimum Number (5) 0.00000 Lower percentage threshold Percentage (including) net effective position Threshold size Maximum Number (5) 5.00000 Upper percentage threshold Percentage (excluding), net effective position Threshold size; empty for last bucket Liquidity Factor Number (5) 0.00000 Liquidity Factor for lower threshold Minimum (including) Threshold Liquidity Factor Number (5) 0.15000 Liquidity Factor for upper threshold Maximum (excluding), empty for last bucket Threshold

The file should end with a End of file information. The format of the same is described in section 5.3.7.

5.3.5.2 Example

An exemplary file will have the following structure:

EOLC;0.00000;5.00000;0.00000;0.15000 EOLC;5.00000;10.00000;0.15000;0.35000 EOLC;10.00000;15.00000;0.35000;0.75000 EOLC;15.00000;20.00000;0.75000;1.00000 EOLC;20.00000;40.00000;1.00000;1.40000 EOLC;40.00000;60.00000;1.40000;1.60000 EOLC;60.00000;;1.60000; EOSC;0.00000;5.00000;0.00000;0.05000 EOSC;5.00000;10.00000;0.05000;0.25000 EOSC;10.00000;15.00000;0.25000;0.50000 EOSC;15.00000;20.00000;0.50000;0.75000 … *EOF*;P;9999;20120523;EUREX;EUREX;NI;LIQUIDITY FACTORS CONFIG

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5.3.6 “Foreign_Exchange_Rates_Configuration” File Several sets of foreign exchange rates will be provided by Eurex Clearing, which can be identified by the FX set identifier. Each set of foreign exchange rates comprises FX rates for all scenario prices of all risk measure sets.

5.3.6.1 Fields

Section Field name Value type Value example Remark (digits after decimal point) FX FX set String (10) FX1 Defined set of FX rates P Currency pair String (6) USDEUR Only for currency pairs containing a clearing currency C Current Number (12) 1.451000000000 Current exchange rate, used to Exchange Rate convert the neutral scenario RMS Risk measure String (30) RMS1 Risk measure set set Exchange Rate Number (12) 1.431000000000 One exchange rate for each Scenarios scenario price of the risk measure set. Corresponding to the scenario prices, the first exchange rate corresponds to the first scenario, the second exchange rate to the second scenario and so on. To convert a USD value into a EUR value using the currency pair USDEUR, the USD value is multiplied by the exchange rate.

The file should end with a End of file information. The format of the same is described in section 5.3.7.

5.3.6.2 Example

An exemplary file will have the following structure:

FX;FX1 P;USDEUR C;1.451000000000 RMS;RMS1;1.431000000000;1.500100000000;1.357800000000;... RMS;RMS2;1.427500000000;1.309000000000;1.398300000000;… … P;GBPEUR C;0.850000000000 RMS;RMS1;0.875100000000;0.764100000000;0.790100000000;… RMS;RMS2;0.894100000000;0.714400000000;0.890100000000;…

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… P;USDCHF C;1.623100000000 RMS;RMS1;1.501003000000;1.621000000000;1.470091000000;… RMS;RMS2;1.230001000000;1.600342000000;1.100531000000;… … P;GBPCHF C;1.100001000000 RMS;RMS1;1.123001000000;1.321009000000;1.100791000000;… RMS;RMS2;1.230012000000;1.120034000000;1.120003000000;… … FX;FX2 P;USDEUR C;1.650010000000 RMS;RMS1;1.330010000000;1.700001000000;1.470078000000;… RMS;RMS2;1.500275000000;1.400096000000;1.893001000000;… … P;GBPEUR C;0.750000000000 RMS;RMS1;0.910051000000;0.820021000000;0.795001000000;… RMS;RMS2;0.700941000000;0.810044000000;0.910001000000;… … P;USDEUR; C;1.530031000000 RMS;RMS1;1.400013000000;1.670030000000;1.573001000000;… RMS;RMS2;1.100041000000;1.520042000000;1.120031000000;… … P;GBPCHF C;1.100001000000 RMS;RMS1;1.120031000000;1.320019000000;1.170091000000;… RMS;RMS2;1.230012000000;1.120034000000;1.120003000000;… … *EOF*;P;2;20120523;EUREX;EUREX;OI;FOREIGN EXCHANGE RATES CONFIG

5.3.7 End of File marker The end of file marker would be the last line in file. For technically splitted files, this will be the last record in the last split

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5.3.7.1 Fields

The following fields are included in this file: Section Field name Value type Value example Remark (digits after decimal point) File end String (5) *EOF* Static field ‘*EOF*’ marker Environment String (1) P Provides the environment type type information. P - Production S - Simulation File Counter String (8) 99999999 Contains the number of records. - Series for theo price File - Risk measure set (RMS lines)for risk measure config file - Risk methods(RM lines) for risk measure aggr. File - Number of records, excluding the EOF record, for Market Capacities - Number of records, excluding the EOF record, for liquidity factors config files - Number of FX sets(FX lines) for Foreign exchange rates config file. Current String(8) 20120907 Current business day in business day YYYYMMDD format Clearing String(5) EUREX Clearing member for whom the file member is created. "EUREX" for the non member specific file.

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Section Field name Value type Value example Remark (digits after decimal point) Non-Clearing String (5) EUREX Non Clearing member for whom Member the file is created. "EUREX" for the non member specific file. File Content String (2) NI NI - For non open interest file. type OI for open interest file For all files except the theoretical price file, this value would be NI. File Description String (50) Theoretical prices THEORETICAL PRICES AND and instrument INSTRUMENT CONFIG config RISK MEASURE CONFIG RISK MEASURE AGGREGATION CONFIG MARKET CAPACITIES CONFIG LIQUIDITY FACTORS CONFIG FOREIGN EXCHANGE RATES CONFIG

5.3.7.2 Example

*EOF*;P;99999999;20120523;EUREX;EUREX;OI;THEORETICAL PRICES AND INSTRUMENT CONFIG

5.4 Algorithmic Description of the Initial Margin Calculation The following algorithmic description explains the necessary steps to calculate the initial margins based on the input files described in section 5.3.

All steps and their corresponding sub-steps can be found in the spreadsheet containing the exemplary calculation ([4] in appendix 6.1).

5.4.1 Step 1: Calculation of Profit and Loss Distributions Input:

 File: “Theoretical_Prices_and_Instrument_Configuration”

 File: “Foreign_Exchange_Rates_Configuration”

 Portfolio Data from Clearing Member

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Output:

 Profit and loss distributions in form of profit and loss vectors for every liquidation group split within a clearing member's portfolio separated by scenario subsamples for every scenario type41

Relevant Sections in chapter 3:

 Section 3.3.1

 Section 3.3.2

 Section 3.3.3

Sub-steps:

(1) Divide all scenario prices (section SP) from the “Theoretical_Prices_and- _Instrument_Configuration” file for every given risk measure set (section RMS) and every instrument in the clearing member's portfolio into the scenario subsamples. The number of scenario subsamples is given by the field holding period (section LH). The scenario prices are assigned to alternating scenario subsamples, i.e. the first scenario price is assigned to the first scenario subsample, the second scenario price to the second scenario subsample and so on. (2) Calculate profit and loss vectors for every position in the clearing members portfolio based on the scenario prices. The profit and loss vectors are calculated separately for each scenario subsample using the scenario prices and the price for the neutral scenario as given in the theoretical prices and instrument description file and the clearing member's positional data as well as the trade unit value of the instrument. In case a liquidation group consists entirely of instruments denominated in the same currency the profit and loss vectors will be calculated in product currency42. Otherwise the profit and loss vectors of these positions need to be calculated in the clearing currency chosen by the clearing member. In that case, the scenario prices are multiplied with or divided by the corresponding scenario FX rate43 and the current price is multiplied with of divided by the current FX rate both given in the file “Foreign_Exchange_Rate_Configuration”44. The set of FX rates utilized for the currency conversion is defined in section FX. The instrument currency is given in the file “Theoretical_Prices_and_Instrument_Description”. (3) Calculate profit and loss distribution for the liquidation group splits within the portfolio of the clearing member using the profit and loss distributions for the positions as calculated in sub- step 2 and the mapping of the instruments to the liquidation group as given in the “Theoretical_Prices_and_Instrument_Configuration” file for all scenario subsamples and all risk measure sets by adding up the profit and loss vectors for all positions from sub-step 2.

41. Currently two scenario types - filtered historical and stressed scenarios. Further scenario types may be introduced at a later time at the discretion of Eurex Clearing. In case further scenario types are introduced the necessary additional scenario prices will also be provided by Eurex Clearing. 42. Compare to section 4.2 43. i.e. the first scenario price is multiplied with or divided by the first FX rate for the respective risk measure set, the second scenario price by the second FX rate and so on 44. The file “Foreign_Exchange_Rate_Configuration” only contains currency pairs, in which one currency is a clearing cur- rency (currently Euro or Swiss Franc). In case other currency pairs are needed, the cross rates have to be calculated as described in section 5.1.7.

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5.4.2 Step 2: Calculation of the Market Risk Components for all Liquidation Groups Input:

 Profit and loss distributions for every liquidation group split separated by scenario subsamples for all risk measure sets calculated in step 1

 File: “Risk_Measure_Configuration”

Output:

 Market risk measures (and scaled market risk measures if robustness enhancement is used) for every liquidation group split for every scenario subsample for the filtered historical scenar- ios and the stressed scenarios

Relevant Sections in chapter 3:

 Section 3.3.4

 Appendix: Section 6.2 (Calculation of VaR figures)

Sub-steps:

(1) Get the risk measure specifications for every risk measure set “Risk_Measure_Configuration” file for each relevant liquidation group. (2) Calculate risk measures for all liquidation group splits and scenario subsamples using their respective profit and loss distributions (from step 1) based on filtered historical scenarios and the risk measure details given in the “Risk_Measure_Configuration”. The method to calculate the VaR figures can be found in the appendix (section 6.2). Risk measures are calculated for every risk measure set, for which scenario prices are provided in the theoretical price file. (3) For every risk measure that uses robustness enhancement, calculate the scaled risk measure by multiplying the original risk measure from sub-step 2 with the respective scaling factor from the “Risk_Measure_Configuration” file.

5.4.3 Step 3: Calculation of the Correlation Break Adjustment Input:

 Liquidation groups' profit and loss distributions for all scenario subgroups of all risk measure sets, for which a correlation break adjustment will be calculated.

 File: “Risk_Measure_Configuration”

Output:

 Correlation Break Adjustment for every scenario subgroup for all liquidation group splits and all risk measure sets for which a correlation break adjustment will be calculated

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Relevant Sections in chapter 3:

 Section 3.4.1

Sub-steps:

(1) Get correlation break specifications for all risk measures in the “Risk_Measure_Configuration” file (2) Calculate risk measures based on profit and loss distributions for all risk measure sets for which the correlation break adjustment will be applied. The confidence level of the risk measures is given in the correlation break specifications of the “Risk_Measure_Configuration” file and can be different from the confidence level calculated in step 2. (3) Calculate risk measures over the time-windows using the specifications given in “Risk_Measure_Configuration” file for every time-window separately for every scenario subgroup of the filtered historical scenarios. The size of each time-window is given in the correlation break specifications in the risk measure configuration file. The following figure illustrates the time-windows, the offset and the time-window length.

Full scenario subgroup

Sub-Window 1 VaR T1 Sub-Window 2 VaR T2 Sub-Window 3 VaR T3 … … …

Length of time-window (e.g. 60 scenarios)

Figure 8: Illustration of time-windows, length of time-windows and offset between time-windows

(4) Compute the squared deviations of the risk measure for every time-window from the respective risk measure for the full scenario subsample calculated in sub-step 3. In case the VaR for the full scenario subsample is more conservative than the VaR for the time-window, the respective squared deviation is set to zero and the time-window will be skipped. The squared deviation calculated in sub-step 4 are summed up separately for each scenario subsample and divided by the number of time-windows, for which the risk measure exceeds the risk measure of the respective full scenario subsample. The mean excess risk measures are the square roots of these quotients. The mean excess risk measures are furthermore scaled by the kappa factor κ given in the file “Risk_Measure_Configuration”. (5) The correlation break adjustments for every scenario subsample and every liquidation group are given by the scaled mean excess risk measure capped by lower and upper bounds multiplied with the pure market risk component of the liquidation group split and scenario subsample as calculated in step 2.

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5.4.4 Step 4: Calculation of the Compression Error Adjustment Input:

 File: “Theoretical_Prices_and_Instrument_Configuration” compression errors for all risk mea- sure sets

 Portfolio data from clearing member

Output:

 Compression Error Adjustment separated by scenario subsample for all risk measure sets and all liquidation group splits

Relevant Sections in chapter 3:

 Section 3.4.2

Sub-steps:

(1) Get the compression errors for every instrument in the clearing member's portfolio from the theoretical price file in the currency of the initial margin. (2) Aggregate compression errors for all positions using the clearing member’s portfolio composition and the liquidation group information by summing up the absolute compression error adjustments position-wise taking into account the trade unit value (see formula in section 3.4.2).

5.4.5 Step 5: Calculation of the Liquidity Risk Component Input:

 File: “Risk_Measure_Configuration” (for every relevant liquidation group split)

 File: “Market_Risk_Aggregation_Configuration” (for every relevant liquidation group split)

 File: “Market_Capacities_Configuration”

 File: “Liquidity_Factors_Configuration”

 File: “Theoretical_Prices_and_Instrument_Configuration”

 Portfolio data from clearing member

Output:

 Liquidity Risk Component for every liquidation group split

Relevant Sections in chapter 3:

 Section 3.5

Sub-steps:

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(1) Get the following information from the input file “Theoretical_Prices_and_- Instrument_Configuration”: liquidity class, time-to-expiry bucket, moneyness bucket, risk bucket, liquidation group, liquidation group split, neutral scenario and the TUV as well as number of contracts from the member's portfolio data. Additionally for liquidation group splits consisting of instruments with different currencies, the FX rates neutral scenario have to be taken from “Foreign_Exchange_Rates_Configuration” File (2) Get market capacities and bid-ask spreads for all relevant product types, time-to-expiry buckets and in case of options moneyness buckets from input file “Market_Capacities_Configuration”. The liquidity premiums and market capacities of a position can be retrieved using the product type, put call flag, time to expiry bucket and - for options - the moneyness bucket. (3) Calculate the net gross ratio for every position for each risk bucket using formula from section 3.5.1. (4) Calculate relative market size for each position using the data collected in sub-step 1 and the market capacities for every instrument in the clearing member's portfolio obtained in sub-step 2. The relative market size of a position is given by the ratio of its absolute position size (i.e. absolute value of the number of contracts) divided by the market capacity of the instrument. The market capacity of an instrument can be retrieved using the product information and risk bucket found in the "Theoretical_Prices_and_Instrument_Configuration" and the "Market_Capacities_Configuration" file. (5) Calculate the net effective relative position size by multiplying the relative market size of a position with the net gross ratio from sub-step 3. (6) Get VaR on instrument level in the required currency (i.e. product currency in case all instruments are denominated in the same currency, clearing currency otherwise) from section IVAR. Conditional on the clearing members position (long/short), the record with the corresponding “Long short Indicator” (L/S) has to be taken from the IVAR section. Calculate positional VaR figures by multiplication with the trade unit value (TUV) and the net effective position size taking into account the net gross ratio calculated in sub-step 3. These positional VaR figures will be used to calculate the market risk element of the positional liquidity risk component (7) Get liquidity factor table from Liquidity Factor file for all asset classes relevant for the clearing member’s portfolio. (8) Interpolate45 the liquidity factors linearly from the liquidity factor table for each position depending on the net effective relative position size (sub-step 5). If the relative position size is higher than the last bucket the last liquidity factor will be used. Calculate liquidity risk component on a positional level using the aggregated positional market risk measures for each position, the liquidity factors and the liquidity premiums as well as the clearing member’s positional data. For the calculation of the liquidity premium the current instrument price (and hence liquidity premium) must be converted to the target currency using the FX rate neutral scenario (not necessary if all instruments in the liquidation group split are denominated in the same currency, see section 4.2). (9) In order to calculate the diversification factor for every liquidation group split, the additional instrument VaRs (AIVAR) are retrieved from the theoretical price file in target currency of the margin. Conditional on the clearing members position (long/short) for each instrument in the liquidation group split, the corresponding records (field: Long short Indicator) have to be

45. The method to interpolate the liquidity factors is described in the appendix in section 6.3 and illustrated in the example calculated in Excel.

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taken. The positional VaR figures used for the calculation of the diversification factor are calculated by multiplying the additional instrument VaR figures with the trade unit value (TUV) and the absolute value of the position size of each instrument46. The market risk measures for the liquidation group splits are recalculated using the risk measure specifications for the liquidity risk component of each relevant liquidation group split. The aggregation of the market risk measures is defined in risk measure aggregation specification for the corresponding risk measure set. (10)The alpha factor for each liquidation group split is calculated by dividing the aggregated market risk measures for the liquidation group splits by the sum of the positional VaR figures obtained earlier for each position within one liquidation group split. In case the calculated alpha factor is smaller than the minimum alpha factor (as given in the risk measure specification of the liquidity risk component for every liquidation group split), the minimum alpha factor is used. (11)Aggregate the liquidity risk component for a liquidation group split by summing the liquidity risk components for each position of the liquidation group split multiplied by the liquidation group split’s alpha factor.

5.4.6 Step 6: Calculation of the Initial Margin Figures Input:

 Market risk measures (without model error adjustments) for all liquidation group splits for every scenario subsample for all risk measure sets (e.g. filtered historical and stressed) calcu- lated in step 2

 Correlation Break Adjustments for every scenario subsample of the filtered historical scenarios for all liquidation group splits calculated in step 3

 Compression Error Adjustment for every scenario subsample for all risk measure sets calcu- lated in step 4

 Liquidity Risk Components for every liquidation group split calculated in step 5

 File: “Market_Risk_Aggregation_Configuration”

Output:

 Initial margins for all liquidation group splits

Relevant Sections in chapter 3:

 Section 3.6

Sub-steps:

(1) Get information from market risk aggregation file for the aggregation of the historical and stressed market risk measures and the aggregation of the scenario subsamples.

46. Note that the actual position size is used instead of the net effective position size used to calculate the position-wise liquidity components

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(2) Add model error adjustments to the pure market risk measures separately for each scenario subsample. Aggregate the scenario subsamples for all risk measure sets and all liquidation group splits including the relevant model errors using the information from sub-step 1. This sub-step leads to one risk measure per risk measure set including the model error adjustments for every liquidation group. (3) Aggregate the market risk measures calculated in sub-step 2 to obtain aggregated market risk measures for every liquidation group split including all model error adjustments. The stressed and historical risk figures are weighted using the factor given in the market risk aggregation file and the aggregation function given in the market risk aggregation specification. This sub-step leads to the aggregated market risk components for every liquidation group split. (4) The initial margin is calculated by adding a liquidation group split's liquidity risk component to its aggregated market risk component.

5.4.7 Step 7: Aggregation of the overall Initial Margin Figure Input:

 Initial margin figures for all liquidation groups splits

Output:

 Aggregated initial margin figure

Sub-steps:

(1) The clearing member's overall initial margin figure is calculated by summing the initial margin figures for all liquidation group splits.

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6Appendix

6.1 Related Documents and Files (1) “Quantitative Risk Management”, Alexander McNeil, Rüdiger Frey and Paul Embrechts, Princeton University Press (2) “VaR Without Correlations for Portfolios of Derivatives Securities”, Giovanni Barone-Adesi, Kostas Giannopoulos and Les Vosper, Journal of Futures Markets 19:583-602, 1999 (3) “Risk-Based-Margining”, Eurex, 2007 (4) “Eurex Clearing Prisma_User Guide Sample Calculations.xlsx”, Eurex Clearing, 2011 (5) “Eurex Clearing Prisma OTC IRS User Guide”, Eurex Clearing, 2011

6.2 Calculation of VaR Figures The VaR figures mentioned in section 3 are quantiles of profit and loss distributions. The VaR at a confidence level α is the (100%-α) quantile of the profit or loss distribution, i.e. the loss that will not be surpassed with a probability of (100%-α).

VaR

VaR at 99%

Profit and Losses

Figure 9: VaR Figure for a confidence level of 99%

The profit or loss distribution can be expressed as a vector, in which each element represents the profit or loss calculated from a given set of scenario prices and current prices.

Each component of the in ascending order sorted profit or loss vector represents a specific quantile of the empirical distribution. The quantile represented by the i-th component of the sorted profit or loss vector can be calculated according to the following formula:

ͳͲͲΨሺͲǤͷ ൅ ݅ െ ͳሻ ݍ ൌ ௜ ݈

In case the (100%-α) quantile is exactly represented by a single component of the subsample profit or loss vector, this component will be the VaR figure.

In case the (100%-α) quantile lies between two quantiles of the profit or loss distribution, it will

be interpolated linearly using the next highest (q+) and next lowest quantile (q-) of the profit and

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loss distribution and the associated components of the profit and loss vector, denotes as (P&Lq+) and (P&Lq-) according to the following formula:

ݍሻ െןሻ ሺͳͲͲΨെןെ ሺͳͲͲΨെ ݍ ା ି ܸܴܽఈ ൌሺ ܲƬܮ௤ష ൅ ܲƬܮ௤ାሻήሺെͳሻ ݍା െݍି ݍା െݍି In case (100-α) is smaller than the quantile associated with the first component, the VaR will be given as the first component. In case it is bigger than the quantile associated with the last component, the VaR will be given as the last component.

A positive VaR figure indicates a loss. The VaR figures utilized for the calculation of the initial margin will always be bounded by zero. Every negative VaR (i.e. a gain) will be set to zero.

Examples:

The following sorted profit or loss vector consisting of 5 elements is given

i P&L vector Quantile: qi components 1 -4000 100*(0.5-1+1)/5=10 2 -3800 100*(0.5-1+2)/5=30 3 -3700 50 4 -3500 70 5 -3200 90

In the following example the VaR90 figure is given as the first component of the profit or loss vector since it exactly represents the 10% quantile of the profit or loss distribution. Therefore the VaR figure is given as47:

VaR90=4000

In order to calculate the VaR80 figure, an interpolation is necessary as the 20% quantile is not directly represented by any component of the profit and loss vector. The next highest (lowest) quantile represented is 30% (10%). Therefore the VaR is given as the linear interpolation according to the following formula: ͵Ͳ െ ʹͲ ʹͲ െ ͳͲ ܸܴܽ ൌ ͶͲͲͲ ή ൅ ͵ͺͲͲ ή ൌ ͵ͻͲͲ ଼଴ ͵Ͳ െ ͳͲ ͵Ͳ െ ͳͲ

In case the VaR shall be calculated at a 95% confidence level, it will be given by the first component as the quantile represented by the first component is higher than 5%.

47. The VaR represents a loss. Therefore a positive VaR indicates a loss. All negative VaR figures will be set to zero.

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6.3 Rounding and Precision of Margin Figures Eurex Clearing internally calculates the margin figures and all intermediate results with double precision. In order to allow the members and the vendors to reproduce the Prisma’s margin figures multiple transparency enabler files are generated. In two of them (Theoretical_Prices_and_Instrument_Configuration and Foreign_Exchange_Rates_Configuration) Prisma reports theoretical prices and exchange rates needed for the computation of the margin. Those values are stored with 6 decimals (FX rates are reported with 12 decimals). However, for the calculation in Prisma double precision is used. Thus, in case of large position size and high TUV rounding differences may occur. The following areas are affected:

 Market Risk calculation: the P&Ls are calculated from rounded scenario prices (in case of cur- rency conversion the rounded scenario FX rate is used) multiplied by the net risk position size and the TUV.

 Compression error add-on: the rounded compression error is multiplied by the net risk posi- tion size and the TUV

 Liquidity add-on: the position risk figure is calculated from the rounded instrument VaR multi- plied by the net risk position size and the TUV

More precisely, if the total position size (net position size * TUV) is 1 000 000, a difference of cents can be expected in each of the mentioned areas. The values for a position will be exact in case of total position size less than 10 000. However, on the portfolio level due to aggregation effects a difference may occur.

6.4 Calculation of the Median The median of a sample x containing n observations is calculated according to the following formula:

݋݀݀ݏ݅݊ ሻ ǡۀ௡Ȁଶڿݔሺ ሺݔሻ ൌ ቐͳ݊ܽ݅݀݁݉ ௡ ௡ ݒ݁݊݁ݏ݅݊ ή൬ݔቀ ቁ ൅ݔቀ ାଵቁ൰ ǡ ʹ ଶ ଶ

Where:

 x(i) is the i-th value of the ordered observations x

 j is the smallest integer not smaller than j

Example:

A sample x=(5,2,8,1,6) containing five observations is given.

The median is:

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median(x)=x(5/2)=x(3)=5

For an even sample x=(4,2,1,3) the median is given as:

median(x)=1/2*(x(2)+x(2+1))=2.5

6.5 Interpolation of Liquidity Factors Liquidity factors for an asset class are interpolated linearly based on the relative size of a position and the values of the liquidity factors of the respective upper and lower thresholds surrounding the relative position size.

The interpolated liquidity factor is given by the formula:

݄݈ܶ ݑ݄ܶ െ ܱܲܵ ܱܲܵ െ ܮܨ ൌܮܨ ή ൅ܮܨ ή ݄݈ܶ ௜௡௧௘௥௣௢௟௔௧௘ௗ ௟் ݑ݄ܶ െ ݈݄ܶ ௨் ݑ݄ܶ െ

Where:

 LFinterpolated is the interpolated liquidity factor

 LFlT is the liquidity factor associated with the lower threshold

 LFuT is the liquidity factor associated with the upper threshold

 uTh is the value of the upper threshold (i.e. 5%)

 lTh is the value of the lower threshold (i.e. 0%)

 POS is the relative size of the position (i.e. 3%)

In case the relative market size is higher than the highest threshold given in the liquidity table, the liquidity factor will be given by the highest liquidity factor available.

Example:

The relative size of a position is 3% of the market capacity. The surrounding lower and upper threshold of the liquidity table is 0% and 5%. For the lower threshold a liquidity factor of 0 is assumed. For the upper bound a liquidity factor of 0.15 is given. The interpolated liquidity factor is therefore 0.09.

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LF (Lower Threshold): LF (Upper Threshold): 0 0.15

Lower Threshold: 0% Upper Threshold: 5%

Rel. Position Size: 3%

Interpolated Liquidity Factor: (0*(5%-3%)+0.15*(3%-0%))/(5%-0%)=0.09

Figure 10: Liquidity Factor Interpolation

6.6 Additional Files The following files are not necessary for the calculation of the initial margin, but will be provided by Eurex Clearing to increase the transparency.

6.6.1 “Asset_Class_Information” File The following file contains the mapping of the asset class numbers used in the files described in section 5.3 and the actual asset class names. Section Field name Value Type Value example Remark Liquidity String (24) EFLC Class Bucket Description String (255) “Equity futures (large cap)”

Example:

BF;Bund futures EFLC;Equity futures (large cap) … …

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6.6.2 “TTE_Bucket_Information” File This file contains the description of the time-to-expiry buckets used in the files described in section 5.3. Section Field name Value Type Value example Remark Product ID String (4) ODAX Put Call Flag String (1) C C - Call P - Put Empty for Futures TTE_Bucket ID String (20) ODAX_C_0 TTE Bucket ID Min TTE Number (0) 0 Minimum business days to expiry, the minimum is included in the TTE bucket. Max TTE Number (0) 14 Maximum business days to expiry, the maximum is excluded from the TTE bucket, empty for last bucket.

Example:

ODAX;C;ODAX_C_0;0;3 ODAX;C;ODAX_C_1;3;6 ODAX;C;ODAX_C_2;3;6 …

6.6.3 “Moneyness_Bucket_Information” File The following file describes the moneyness buckets. Section Field name Value Type Value example Remark Product ID String (4) ODAX Put Call Flag String (1) C C - Call P - Put Moneyness String (20) ODAX_C_1 Identifier: Bucket ID Product ID & “_” & Put Call Flag & “_” & Min modified moneyness Min Mod. Number(5) 99.00000 Lower bound modified moneyness1 Moneyness bucket, the minimum value is included in the moneyness bucket, empty for first bucket Max Mod. Number(5) 101.00000 Upper bound modified moneyness Moneyness bucket, the maximum value is excluded from the moneyness bucket, empty for last bucket ܵ 1.The modified moneyness is defined as Ž‘‰ሺ ൗሻ . ݉݊ ൌ ܭ ξݐ

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Example:

ODAX;C;ODAX_C_1;;101.12345 ODAX;C;ODAX_C_2;101.12345;103.12345 ODAX;C;ODAX_C_3;103.12345;105.12345 ODAX;C;ODAX_C_4;105.12345; …

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7 Glossary

Compression error adjustment The compression error adjustment is a model adjustment to account for the model error when calculating instrument prices such as the representation of volatility surfaces by a reduced set of risk factors or the use of benchmark risk factors in case an insufficient amount of market data is available for an instrument's actual risk factors.

Correlation break adjustment The correlation break adjustment is a model error adjustment accounting for non-stationarities of the time series of scenario prices such as changes in the correlation structure between risk factors.

Current liquidating margin Current liquidating margin is collected from buyers or sellers of bonds and equities. The current liquidating margin covers losses that would occur in case a position has to be closed out immediately. The methodology to calculate the current liquidating margin remains unchanged by Eurex Clearing Prisma.

Eurex Clearing Prisma Eurex Clearing Prisma replaces the former Risk based Margining (RBM) methodology to calculate the initial margin (“Additional Margin” under RBM) to be posted by a clearing member.

Filtered historical simulation Historical simulation where scenario risk factor returns are derived by volatility-filtering to improve the stationarity properties of the simulation sample.

Holding period Within the holding period all instruments of a liquidation group can be liquidated. The default value for the holding period will be set by Eurex Clearing. Usually a holding period of approximately 3 to 5 days is appropriate. The exemplary calculations shown in this document are based on a holding period of 2 days in order to provide a concise presentation.

Initial margin The initial margin is a forward looking margin component (RBM: additional margin + and therefore a provision for future potential losses over the future spread margin) holding period of a defaulting clearing member's positions. The initial margin will be calculated separately for every liquidation group split. The new methodology to calculate the initial margin is a key component of Eurex Clearing Prisma.

Instrument Any financial instrument such as an option series or a futures contract will be referred to as instrument in this document.

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Liquidation group A liquidation group is a pre-defined set of instruments. Liquidation groups are defined on clearing house level across all respective members. In case of a clearing member default these liquidation groups will be liquidated separately while the positions within a liquidation group are intended to be auctioned together. Expiring positions within each liquidation group will be treated separately as immediate actions have to be performed (compare to definition of liquidation group splits).

Liquidation group split Liquidation groups are further divided into liquidation group splits according to the assumed underlying holding period of the respective liquidation group. Instruments with a time to expiry less than the defined holding period, e.g. of no more than 5 days, will be mapped to this distinct liquidation group split as they are treated separately from instruments with a longer time to expiry in the default management process. Margin offsets are granted for instruments within a liquidation group split.

Liquidity Risk Component The liquidity risk component is designed to capture the effect of adverse price movements when liquidating portfolios.

Market risk component of The market risk component is part of the initial margin. Initial Margin (MRIM) The market risk component consists of the pure market risk component based on tail risk measures of the liquidation group splits' profit and loss distributions and several model error adjustments.

Model error adjustments Model error adjustments mitigate possible model simplifications encountered when calculating the initial margin's market risk component. The following model error adjustments are included in the initial margin: - Correlation Break Adjustment - Compression Error Adjustment The model error adjustments lead to a more adequate initial margin figure.

Modified moneyness The modified moneyness of an option is the standard moneyness divided by the square root of the time to expiry. Options are grouped into risk buckets based on their time to expiry and the modified moneyness.

Net effective position size The net effective position size is used for the calculation of the liquidity component and determined by multiplying the actual position size (i.e. the number of contracts) with the net gross ratio.

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Net gross ratio The net gross ratio is utilized to calculate the net effective position size used for the calculation of the liquidity component. The net gross ratio is determined by dividing the sum of the actual position sizes by the sum of the absolute position sizes within a risk bucket.

Principal Component Analysis A procedure that uses an orthogonal transformation to (PCA) convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables called principal components. Often the first few principal components can explain most of the variability of given correlated observations.

Premium margin A premium margin must be deposited by the writer of an option to cover potential losses that could be incurred if the clearing house were forced to liquidate the position today. The premium margin is credited to the buyer of the option. The premium margin is continuously adjusted as the option price fluctuates. The methodology to calculate the premium margin remains unchanged by Eurex Clearing Prisma.

Profit and loss distributions Profit and loss distributions are vectors of profits and losses for an instrument or liquidation group splits. The profit or loss distribution of an instrument is calculated based on the current price of the instrument and a set of scenario prices. The profit or loss distribution of a liquidation group split is calculated by aggregating the profit or losses of all instruments within a liquidation group split.

Risk bucket Instruments with similar characteristics with respect to their time to expiry and their modified moneyness (for options only) are grouped into risk buckets. For each risk bucket a net gross ratio will be calculated to determine the effective position size used for the calculation of the liquidity adjustment.

Risk factor One or several risk factors are responsible for changes in prices of financial instruments. Examples for risk factors are equity prices, interest rates or implied volatilities.

Risk measure The term risk measure refers to the mathematical operation of assigning a number to quantify risk from a given distribution of possible price changes. The risk measure most commonly used in the Eurex Clearing Prisma methodology is the Value- at-Risk.

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Scenario prices To calculate the initial margin of a liquidation group split, risk measures are calculated based on scenario prices. The set of scenario prices comprises approximately 750 scenarios based on a Filtered Historical Simulation (see [2]) and 250 scenarios observed during stress periods mainly characterized by a high volatility of the relevant risk factors. The scenario prices reflect price returns according to a liquidation group split's holding period.

Scenario subsample The scenario prices are divided into several subsamples to avoid artificial statistical effects resulting from overlapping time periods that would violate the assumptions of the calculated risk figures. Therefore each risk figure is calculated on scenario subsample level and subsequently aggregated to an overall risk figure. The number of subsamples depends on a liquidation group split's holding period.

Stressed periods The stressed periods are a union of fixed historical time- intervals representing stressed market conditions characterized by a high volatility of the relevant risk factors.

Subportfolio In the following document a subportfolio is referred to as a clearing member's set of positions that belong to the same liquidation group split.

Trade Unit Value (TUV) The Trade Unit Value measures the size of one contract. It is calculated as tick size divided by tick value multiplied by trading unit.

Value-at-Risk (VaR) Risk measure based on a quantile of a profit and loss distribution for a given confidence level (see McNeil 2005 et al, Chapter 1 and 2 [1]).

Variation margin Profits and losses of all open positions encountered during a trading day are consecutively booked into an account for all products handled on a mark-to-market basis. Using variation margin, profits and losses that arise due to the price fluctuations are offset daily. Variation margins are applied to futures, future style options and interest rate swaps.

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