Disclosure Annex for Commodity Derivative Transactions
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V. Black-Scholes Model: Derivation and Solution
V. Black-Scholes model: Derivation and solution Beáta Stehlíková Financial derivatives, winter term 2014/2015 Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava V. Black-Scholes model: Derivation and solution – p.1/36 Content Black-Scholes model: • Suppose that stock price follows a geometric ◦ S Brownian motion dS = µSdt + σSdw + other assumptions (in a moment) We derive a partial differential equation for the price of ◦ a derivative Two ways of derivations: • due to Black and Scholes ◦ due to Merton ◦ Explicit solution for European call and put options • V. Black-Scholes model: Derivation and solution – p.2/36 Assumptions Further assumptions (besides GBP): • constant riskless interest rate ◦ r no transaction costs ◦ it is possible to buy/sell any (also fractional) number of ◦ stocks; similarly with the cash no restrictions on short selling ◦ option is of European type ◦ Firstly, let us consider the case of a non-dividend paying • stock V. Black-Scholes model: Derivation and solution – p.3/36 Derivation I. - due to Black and Scholes Notation: • S = stock price, t =time V = V (S, t)= option price Portfolio: 1 option, stocks • δ P = value of the portfolio: P = V + δS Change in the portfolio value: • dP = dV + δdS From the assumptions: From the It¯o • dS = µSdt + σSdw, ∂V ∂V 1 2 2 ∂2V ∂V lemma: dV = ∂t + µS ∂S + 2 σ S ∂S2 dt + σS ∂S dw Therefore: • ∂V ∂V 1 ∂2V dP = + µS + σ2S2 + δµS dt ∂t ∂S 2 ∂S2 ∂V + σS + δσS dw ∂S V. Black-Scholes model: Derivation and solution – p.4/36 Derivation I. -
Form Dated March 20, 2007 Swaption Template (Full Underlying Confirmation)
Form Dated March 20, 2007 Swaption template (Full Underlying Confirmation) CONFIRMATION DATE: [Date] TO: [Party B] Telephone No.: [number] Facsimile No.: [number] Attention: [name] FROM: [Party A] SUBJECT: Swaption on [CDX.NA.[IG/HY/XO].____] [specify sector, if any] [specify series, if any] [specify version, if any] REF NO: [Reference number] The purpose of this communication (this “Confirmation”) is to set forth the terms and conditions of the Swaption entered into on the Swaption Trade Date specified below (the “Swaption Transaction”) between [Party A] (“Party A”) and [counterparty’s name] (“Party B”). This Confirmation constitutes a “Confirmation” as referred to in the ISDA Master Agreement specified below. The definitions and provisions contained in the 2000 ISDA Definitions (the “2000 Definitions”) and the 2003 ISDA Credit Derivatives Definitions as supplemented by the May 2003 Supplement to the 2003 ISDA Credit Derivatives Definitions (together, the “Credit Derivatives Definitions”), each as published by the International Swaps and Derivatives Association, Inc. are incorporated into this Confirmation. In the event of any inconsistency between the 2000 Definitions or the Credit Derivatives Definitions and this Confirmation, this Confirmation will govern. In the event of any inconsistency between the 2000 Definitions and the Credit Derivatives Definitions, the Credit Derivatives Definitions will govern in the case of the terms of the Underlying Swap Transaction and the 2000 Definitions will govern in other cases. For the purposes of the 2000 Definitions, each reference therein to Buyer and to Seller shall be deemed to refer to “Swaption Buyer” and to “Swaption Seller”, respectively. This Confirmation supplements, forms a part of and is subject to the ISDA Master Agreement dated as of [ ], as amended and supplemented from time to time (the “Agreement”) between Party A and Party B. -
Derivative Markets Swaps.Pdf
Derivative Markets: An Introduction Derivative markets: swaps 4 Derivative markets: swaps 4.1 Learning outcomes After studying this text the learner should / should be able to: 1. Define a swap. 2. Describe the different types of swaps. 3. Elucidate the motivations underlying interest rate swaps. 4. Illustrate how swaps are utilised in risk management. 5. Appreciate the variations on the main themes of swaps. 4.2 Introduction Figure 1 presentsFigure the derivatives 1: derivatives and their relationshipand relationship with the spotwith markets. spot markets forwards / futures on swaps FORWARDS SWAPS FUTURES OTHER OPTIONS (weather, credit, etc) options options on on swaps = futures swaptions money market debt equity forex commodity market market market markets bond market SPOT FINANCIAL INSTRUMENTS / MARKETS Figure 1: derivatives and relationship with spot markets Download free eBooks at bookboon.com 116 Derivative Markets: An Introduction Derivative markets: swaps Swaps emerged internationally in the early eighties, and the market has grown significantly. An attempt was made in the early eighties in some smaller to kick-start the interest rate swap market, but few money market benchmarks were available at that stage to underpin this new market. It was only in the middle nineties that the swap market emerged in some of these smaller countries, and this was made possible by the creation and development of acceptable benchmark money market rates. The latter are critical for the development of the derivative markets. We cover swaps before options because of the existence of options on swaps. This illustration shows that we find swaps in all the spot financial markets. A swap may be defined as an agreement between counterparties (usually two but there can be more 360° parties involved in some swaps) to exchange specific periodic cash flows in the future based on specified prices / interest rates. -
How Much Do Banks Use Credit Derivatives to Reduce Risk?
How much do banks use credit derivatives to reduce risk? Bernadette A. Minton, René Stulz, and Rohan Williamson* June 2006 This paper examines the use of credit derivatives by US bank holding companies from 1999 to 2003 with assets in excess of one billion dollars. Using the Federal Reserve Bank of Chicago Bank Holding Company Database, we find that in 2003 only 19 large banks out of 345 use credit derivatives. Though few banks use credit derivatives, the assets of these banks represent on average two thirds of the assets of bank holding companies with assets in excess of $1 billion. To the extent that banks have positions in credit derivatives, they tend to be used more for dealer activities than for hedging activities. Nevertheless, a majority of the banks that use credit derivative are net buyers of credit protection. Banks are more likely to be net protection buyers if they engage in asset securitization, originate foreign loans, and have lower capital ratios. The likelihood of a bank being a net protection buyer is positively related to the percentage of commercial and industrial loans in a bank’s loan portfolio and negatively or not related to other types of bank loans. The use of credit derivatives by banks is limited because adverse selection and moral hazard problems make the market for credit derivatives illiquid for the typical credit exposures of banks. *Respectively, Associate Professor, The Ohio State University; Everett D. Reese Chair of Banking and Monetary Economics, The Ohio State University and NBER; and Associate Professor, Georgetown University. We are grateful to Jim O’Brien and Mark Carey for discussions. -
5. Caps, Floors, and Swaptions
Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Interest Rate and Credit Models 5. Caps, Floors, and Swaptions Andrew Lesniewski Baruch College New York Spring 2019 A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Outline 1 Options on LIBOR based instruments 2 Valuation of LIBOR options 3 Local volatility models 4 The SABR model 5 Volatility cube A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Options on LIBOR based instruments Interest rates fluctuate as a consequence of macroeconomic conditions, central bank actions, and supply and demand. The existence of the term structure of rates, i.e. the fact that the level of a rate depends on the maturity of the underlying loan, makes the dynamics of rates is highly complex. While a good analogy to the price dynamics of an equity is a particle moving in a medium exerting random shocks to it, a natural way of thinking about the evolution of rates is that of a string moving in a random environment where the shocks can hit any location along its length. A. Lesniewski Interest Rate and Credit Models Options on LIBOR based instruments Valuation of LIBOR options Local volatility models The SABR model Volatility cube Options on LIBOR based instruments Additional complications arise from the presence of various spreads between rates, as discussed in Lecture Notes #1, which reflect credit quality of the borrowing entity, liquidity of the instrument, or other market conditions. -
An Asset Manager's Guide to Swap Trading in the New Regulatory World
CLIENT MEMORANDUM An Asset Manager’s Guide to Swap Trading in the New Regulatory World March 11, 2013 As a result of the Dodd-Frank Act, the over-the-counter derivatives markets Contents have become subject to significant new regulatory oversight. As the Swaps, Security-Based markets respond to these new regulations, the menu of derivatives Swaps, Mixed Swaps and Excluded Instruments ................. 2 instruments available to asset managers, and the costs associated with those instruments, will change significantly. As the first new swap rules Key Market Participants .............. 4 have come into effect in the past several months, market participants have Cross-Border Application of started to identify risks and costs, as well as new opportunities, arising from the U.S. Swap Regulatory this new regulatory landscape. Regime ......................................... 7 Swap Reporting ........................... 8 This memorandum is designed to provide asset managers with background information on key aspects of the swap regulatory regime that may impact Swap Clearing ............................ 12 their derivatives trading activities. The memorandum focuses largely on the Swap Trading ............................. 15 regulations of the CFTC that apply to swaps, rather than on the rules of the Uncleared Swap Margin ............ 16 SEC that will govern security-based swaps, as virtually none of the SEC’s security-based swap rules have been adopted. Swap Dealer Business Conduct and Swap This memorandum first provides background information on the types of Documentation Rules ................ 19 derivatives that are subject to the CFTC’s swap regulatory regime, on new Position Limits and Large classifications of market participants created by the regime, and on the Trader Reporting ....................... 22 current approach to the cross-border application of swap requirements. -
Computation of Binomial Option Pricing Model with Parallel
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by KHALSA PUBLICATIONS I S S N 2 2 7 8 - 5 6 1 2 Volume 11 Number 5 International Journal of Management and Information T e c h n o l o g y Computation Of Binomial Option Pricing Model With Parallel Processing On A Linux Cluster Harya Widiputra Faculty of Information Technology, Perbanas Institute Jakarta, Indonesia [email protected] ABSTRACT Binary Option Pricing Model (BOPM) is one approach that can be utilized to calculate the value of either call or put option. BOPM generally works by building a binomial tree diagram, also known as lattice diagram to explore all possible option values that occur based on the intrinsic price of the underlying asset in a range of specific time period. Due to its basic characteristics BOPM is renowned for its longer lead times in calculating option values while also acknowledged as a technique that can provide an assessment of the most fair option value. Therefore, this study aims to shorten the BOPM completion time of calculating the value of an option by building a computer cluster and presently implement the BOPM algorithm into a form that can be run in parallel processing. As an outcome, a Linux-based computer cluster has been built and conversion of BOPM algorithm so that it can be executed in parallel has been performed and also implemented using Python in this research. Conclusively, results of conducted experiments confirm that the implementation of BOPM algorithm in a form that can be executed in parallel and its application on a computer cluster was able to limit the growth of the completion time whilst at the same time maintain quality of calculated option values. -
Implied Volatility Modeling
Implied Volatility Modeling Sarves Verma, Gunhan Mehmet Ertosun, Wei Wang, Benjamin Ambruster, Kay Giesecke I Introduction Although Black-Scholes formula is very popular among market practitioners, when applied to call and put options, it often reduces to a means of quoting options in terms of another parameter, the implied volatility. Further, the function σ BS TK ),(: ⎯⎯→ σ BS TK ),( t t ………………………………(1) is called the implied volatility surface. Two significant features of the surface is worth mentioning”: a) the non-flat profile of the surface which is often called the ‘smile’or the ‘skew’ suggests that the Black-Scholes formula is inefficient to price options b) the level of implied volatilities changes with time thus deforming it continuously. Since, the black- scholes model fails to model volatility, modeling implied volatility has become an active area of research. At present, volatility is modeled in primarily four different ways which are : a) The stochastic volatility model which assumes a stochastic nature of volatility [1]. The problem with this approach often lies in finding the market price of volatility risk which can’t be observed in the market. b) The deterministic volatility function (DVF) which assumes that volatility is a function of time alone and is completely deterministic [2,3]. This fails because as mentioned before the implied volatility surface changes with time continuously and is unpredictable at a given point of time. Ergo, the lattice model [2] & the Dupire approach [3] often fail[4] c) a factor based approach which assumes that implied volatility can be constructed by forming basis vectors. Further, one can use implied volatility as a mean reverting Ornstein-Ulhenbeck process for estimating implied volatility[5]. -
Arithmetic Variance Swaps
Arithmetic variance swaps Article (Accepted Version) Leontsinis, Stamatis and Alexander, Carol (2017) Arithmetic variance swaps. Quantitative Finance, 17 (4). pp. 551-569. ISSN 1469-7688 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/id/eprint/62303/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher’s version. Please see the URL above for details on accessing the published version. Copyright and reuse: Sussex Research Online is a digital repository of the research output of the University. Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available. Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. http://sro.sussex.ac.uk Arithmetic Variance Swaps Stamatis Leontsinisa and Carol Alexanderb a RwC Asset Management, London b School of Business, Management and Economics, University of Sussex To appear in Quantitative Finance, 2016 (in press) Abstract Biases in standard variance swap rates can induce substantial deviations below market rates. -
Tax Treatment of Derivatives
United States Viva Hammer* Tax Treatment of Derivatives 1. Introduction instruments, as well as principles of general applicability. Often, the nature of the derivative instrument will dictate The US federal income taxation of derivative instruments whether it is taxed as a capital asset or an ordinary asset is determined under numerous tax rules set forth in the US (see discussion of section 1256 contracts, below). In other tax code, the regulations thereunder (and supplemented instances, the nature of the taxpayer will dictate whether it by various forms of published and unpublished guidance is taxed as a capital asset or an ordinary asset (see discus- from the US tax authorities and by the case law).1 These tax sion of dealers versus traders, below). rules dictate the US federal income taxation of derivative instruments without regard to applicable accounting rules. Generally, the starting point will be to determine whether the instrument is a “capital asset” or an “ordinary asset” The tax rules applicable to derivative instruments have in the hands of the taxpayer. Section 1221 defines “capital developed over time in piecemeal fashion. There are no assets” by exclusion – unless an asset falls within one of general principles governing the taxation of derivatives eight enumerated exceptions, it is viewed as a capital asset. in the United States. Every transaction must be examined Exceptions to capital asset treatment relevant to taxpayers in light of these piecemeal rules. Key considerations for transacting in derivative instruments include the excep- issuers and holders of derivative instruments under US tions for (1) hedging transactions3 and (2) “commodities tax principles will include the character of income, gain, derivative financial instruments” held by a “commodities loss and deduction related to the instrument (ordinary derivatives dealer”.4 vs. -
Opposition, CFTC V. Banc De Binary
Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 1 of 30 Kathleen Banar, Chief Trial Attorney (IL Bar No. 6200597) David Slovick, Senior Trial Attorney (IL Bar No. 6257290) Margaret Aisenbrey, Trial Attorney (Mo Bar No. 59560) U.S. Commodity Futures Trading Commission 1155 21 St. NW Washington, DC 20581 [email protected], [email protected], [email protected] (202) 418-5335 (202) 418-5987 (facsimile) Blaine T. Welsh (NV Bar No. 4790) Assistant United States Attorney United States Attorney’s Office 333 Las Vegas Boulevard, Suite 5000 Las Vegas, Nevada 89101 [email protected] (702) 388-6336 (702) 388-6787 (facsimile) UNITED STATES DISTRICT COURT DISTRICT OF NEVADA ) U.S. COMMODITY FUTURES TRADING ) COMMISSION, ) ) Case No. 2:13-cv-00992-MMD-VCF Plaintiff, ) ) PLAINTIFF’S OPPOSITION TO v. ) DEFENDANT’S MOTION TO ) DISMISS COUNTS ONE, THREE ) AND FOUR OF THE COMPLAINT BANC DE BINARY LTD. (A/K/A E.T. ) BINARY OPTIONS LTD.), ) ) Defendant. ) ) 1 Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 2 of 30 The United States Commodity Futures Trading Commission (“CFTC” or “Commission”) opposes Banc de Binary’s Motion to Dismiss Counts I, III and IV of the Complaint (“Defendant’s Motion”),1 and states as follows: I. SUMMARY Since at least May 2012 Banc de Binary Ltd. (A/K/A E.T. Binary Options) (“Banc de Binary” or “Defendant”) has been violating the CFTC’s long-standing ban on trading options contracts with persons located in the United States off of a contract market designated by the CFTC for that purpose (i.e., “off-exchange”). -
Pricing Financial Derivatives Under the Regime-Switching Models Mengzhe Zhang
Pricing Financial Derivatives Under the Regime-Switching Models Mengzhe Zhang A thesis in fulfilment of the requirements the degree of Doctor of Philosophy School of Mathematics and Statistics Faculty of Science, University of New South of Wales, Australia 19th April 2017 Acknowledgement First of all, I would like to thank my supervisor Dr Leung Lung Chan for his valuable guidance, helpful comments and enlightening advice throughout the preparation of this thesis. I also want to thank my parents for their love, support and encouragement throughout my graduate study time at the University of NSW. Last but not the least, I would like to thank my friends- Dr Xin Gao, Dr Xin Zhang, Dr Wanchuang Zhu, Dr Philip Chen and Dr Jinghao Huang from the Math school of UNSW and Dr Zhuo Chen, Dr Xueting Zhang, Dr Tyler Kwong, Dr Henry Rui, Mr Tianyu Cai, Mr Zhongyuan Liu, Mr Yue Peng and Mr Huaizhou Li from the Business school of UNSW. i Contents 1 Introduction1 1.1 BS-Type Model with Regime-Switching.................5 1.2 Heston's Model with Regime-Switching.................6 2 Asymptotics for Option Prices with Regime-Switching Model: Short- Time and Large-Time9 2.1 Introduction................................9 2.2 BS Model with Regime-Switching.................... 13 2.3 Small Time Asymptotics for Option Prices............... 13 2.3.1 Out-of-the-Money and In-the-Money.............. 13 2.3.2 At-the-Money........................... 25 2.3.3 Numerical Results........................ 35 2.4 Large-Maturity Asymptotics for Option Prices............. 39 ii 2.5 Calibration................................ 53 2.6 Conclusion................................. 57 3 Saddlepoint Approximations to Option Price in A Regime-Switching Model 59 3.1 Introduction...............................