Interest Rate Linked Structured Investments
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Interest Rate Options
Interest Rate Options Saurav Sen April 2001 Contents 1. Caps and Floors 2 1.1. Defintions . 2 1.2. Plain Vanilla Caps . 2 1.2.1. Caplets . 3 1.2.2. Caps . 4 1.2.3. Bootstrapping the Forward Volatility Curve . 4 1.2.4. Caplet as a Put Option on a Zero-Coupon Bond . 5 1.2.5. Hedging Caps . 6 1.3. Floors . 7 1.3.1. Pricing and Hedging . 7 1.3.2. Put-Call Parity . 7 1.3.3. At-the-money (ATM) Caps and Floors . 7 1.4. Digital Caps . 8 1.4.1. Pricing . 8 1.4.2. Hedging . 8 1.5. Other Exotic Caps and Floors . 9 1.5.1. Knock-In Caps . 9 1.5.2. LIBOR Reset Caps . 9 1.5.3. Auto Caps . 9 1.5.4. Chooser Caps . 9 1.5.5. CMS Caps and Floors . 9 2. Swap Options 10 2.1. Swaps: A Brief Review of Essentials . 10 2.2. Swaptions . 11 2.2.1. Definitions . 11 2.2.2. Payoff Structure . 11 2.2.3. Pricing . 12 2.2.4. Put-Call Parity and Moneyness for Swaptions . 13 2.2.5. Hedging . 13 2.3. Constant Maturity Swaps . 13 2.3.1. Definition . 13 2.3.2. Pricing . 14 1 2.3.3. Approximate CMS Convexity Correction . 14 2.3.4. Pricing (continued) . 15 2.3.5. CMS Summary . 15 2.4. Other Swap Options . 16 2.4.1. LIBOR in Arrears Swaps . 16 2.4.2. Bermudan Swaptions . 16 2.4.3. Hybrid Structures . 17 Appendix: The Black Model 17 A.1. -
Taking the Risk out of Interest Rate Risk Protecting Countries Against Interest Rate Risk with IBRD Flexible Loans
ASE STUDY Taking the Risk out of Interest Rate Risk Protecting Countries against Interest Rate Risk with IBRD Flexible Loans OVERVIEW Interest rate risk can increase debt- servicing costs, putting pressure on national budgets and forcing countries to impose spending cuts or tax reforms. The World Bank helps countries manage this risk with market-based risk management tools such as the IBRD Flexible Loan (IFL). Over the past 17 years, the World Bank has helped over 40 countries with a combined US$70 billion portfolio use the IFL. Local fisherman in Mexico. Photo credit: Curt Carnemark / World Bank. strategies, many governments establish targets or Background benchmark ranges for key risk indicators to guide borrowing activities and other debt transactions. One Governments borrow from the global financial way that a country can achieve the target mix of markets to fund key development objectives such as fixed-rate versus floating-rate debt is by fixing the high-quality education, clean energy, and needed interest rates on loans. infrastructure. But borrowing at floating interest rates may expose governments to interest rate risk. Countries that have a high percentage of their debt Financing Objectives portfolio in floating interest rates could see interest The IBRD Flexible Loan allows countries to meet payments increase dramatically with the upsurge of several objectives: the reference rate. • Reduce interest rate risk of public debt stock If interest rate risk materializes, countries face higher • Keep the ratio of floating interest rate to fixed debt-servicing costs, which put pressure on the interest rate within the target benchmarks as country’s budget. -
Interest Rate and Credit Models 6
Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Interest Rate and Credit Models 6. Convexity and CMS Andrew Lesniewski Baruch College New York Spring 2019 A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Outline 1 Convexity in LIBOR 2 CMS rates and instruments 3 The uses of Girsanov’s theorem A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Convexity In financial lingo, convexity is a broadly understood and often non-specific term for nonlinear behavior of the price of an instrument as a function of evolving markets. Typically, such convexities reflect the presence of some sort of optionality embedded in the instrument. In this lecture we will focus on a number of convexities which arise in interest rates markets. Convex behavior in interest rate markets manifests itself as the necessity to include convexity corrections to various popular interest rates and they can be blessings and nightmares of market practitioners. From the perspective of financial modeling they arise as the results of valuation done under the “wrong” martingale measure. A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Convexity Throughout this lecture we will be making careful notational distinction between stochastic processes, such as prices of zero coupon bonds, and their current (known) values. The latter will be indicated by the subscript 0. Thus, as in the previous lectures, (i) P0(t; T ) = P(0; t; T ) denotes the current value of the forward discount factor, (ii) P(t; T ) = P(t; t; T ) denotes the time t value of the stochastic process describing the price of the zero coupon bond maturing at T . -
Banca Popolare Dell’Alto Adige Joint-Stock Company
2016 FINANCIAL STATEMENTS 1 Banca Popolare dell’Alto Adige Joint-stock company Registered office and head office: Via del Macello, 55 – I-39100 Bolzano Share Capital as at 31 December 2016: Euro 199,439,716 fully paid up Tax code, VAT number and member of the Business Register of Bolzano no. 00129730214 The bank adheres to the inter-bank deposit protection fund and the national guarantee fund ABI 05856.0 www.bancapopolare.it – www.volksbank.it 2 3 „Wir arbeiten 2017 konzentriert daran, unseren Strategieplan weiter umzusetzen, die Kosten zu senken, die Effizienz und Rentabilität der Bank zu erhöhen und die Digitalisierung voranzutreiben. Auch als AG halten wir an unserem Geschäftsmodell einer tief verankerten Regionalbank in Südtirol und im Nordosten Italiens fest.“ Otmar Michaeler Volksbank-Präsident 4 DIE VOLKSBANK HAT EIN HERAUSFORDERNDES JAHR 2016 HINTER SICH. Wir haben vieles umgesetzt, aber unser hoch gestecktes Renditeziel konnten wir nicht erreichen. Für 2017 haben wir uns vorgenommen, unsere Projekte und Ziele mit noch mehr Ehrgeiz zu verfolgen und die Rentabilität der Bank deutlich zu erhöhen. 2016 wird als das Jahr der Umwandlung in eine Aktien- Beziehungen und wollen auch in Zukunft Kredite für Familien und gesellschaft in die Geschichte der Volksbank eingehen. kleine sowie mittlere Unternehmen im Einzugsgebiet vergeben. Diese vom Gesetzgeber aufgelegte Herausforderung haben Unser vorrangiges Ziel ist es, beste Lösungen für unsere die Mitglieder im Rahmen der Mitgliederversammlung im gegenwärtig fast 60.000 Mitglieder und über 260.000 Kunden November mit einer überwältigenden Mehrheit von 97,5 Prozent zu finden. angenommen. Gleichzeitig haben wir die Weichen gestellt, um All dies wird uns in die Lage versetzen, in Zukunft wieder auch als AG eine erfolgreiche und tief verankerte Regionalbank Dividenden auszuschütten. -
The Role of Interest Rate Swaps in Corporate Finance
The Role of Interest Rate Swaps in Corporate Finance Anatoli Kuprianov n interest rate swap is a contractual agreement between two parties to exchange a series of interest rate payments without exchanging the A underlying debt. The interest rate swap represents one example of a general category of financial instruments known as derivative instruments. In the most general terms, a derivative instrument is an agreement whose value derives from some underlying market return, market price, or price index. The rapid growth of the market for swaps and other derivatives in re- cent years has spurred considerable controversy over the economic rationale for these instruments. Many observers have expressed alarm over the growth and size of the market, arguing that interest rate swaps and other derivative instruments threaten the stability of financial markets. Recently, such fears have led both legislators and bank regulators to consider measures to curb the growth of the market. Several legislators have begun to promote initiatives to create an entirely new regulatory agency to supervise derivatives trading activity. Underlying these initiatives is the premise that derivative instruments increase aggregate risk in the economy, either by encouraging speculation or by burdening firms with risks that management does not understand fully and is incapable of controlling.1 To be certain, much of this criticism is aimed at many of the more exotic derivative instruments that have begun to appear recently. Nevertheless, it is difficult, if not impossible, to appreciate the economic role of these more exotic instruments without an understanding of the role of the interest rate swap, the most basic of the new generation of financial derivatives. -
Derivative Instruments and Hedging Activities
www.pwc.com 2015 Derivative instruments and hedging activities www.pwc.com Derivative instruments and hedging activities 2013 Second edition, July 2015 Copyright © 2013-2015 PricewaterhouseCoopers LLP, a Delaware limited liability partnership. All rights reserved. PwC refers to the United States member firm, and may sometimes refer to the PwC network. Each member firm is a separate legal entity. Please see www.pwc.com/structure for further details. This publication has been prepared for general information on matters of interest only, and does not constitute professional advice on facts and circumstances specific to any person or entity. You should not act upon the information contained in this publication without obtaining specific professional advice. No representation or warranty (express or implied) is given as to the accuracy or completeness of the information contained in this publication. The information contained in this material was not intended or written to be used, and cannot be used, for purposes of avoiding penalties or sanctions imposed by any government or other regulatory body. PricewaterhouseCoopers LLP, its members, employees and agents shall not be responsible for any loss sustained by any person or entity who relies on this publication. The content of this publication is based on information available as of March 31, 2013. Accordingly, certain aspects of this publication may be superseded as new guidance or interpretations emerge. Financial statement preparers and other users of this publication are therefore cautioned to stay abreast of and carefully evaluate subsequent authoritative and interpretative guidance that is issued. This publication has been updated to reflect new and updated authoritative and interpretative guidance since the 2012 edition. -
Pricing Models for Bermudan-Style Interest Rate Derivatives and Options
Erim - 05 omslag Pietersz 9/23/05 1:41 PM Pagina 1 Design: B&T Ontwerp en advies www.b-en-t.nl Print: Haveka www.haveka.nl Pricing models for Bermudan-style interest rate 71 RAOUL PIETERSZ derivatives Bermudan-style interest rate derivatives are an important class of RAOUL PIETERSZ options. Many banking and insurance products, such as mortgages, cancellable bonds, and life insurance products, contain Bermudan interest rate options associated with early redemption or cancella- tion of the contract. The abundance of these options makes evident Pricing models for that their proper valuation and risk measurement are important to banks and insurance companies. Risk measurement allows for off- Bermudan-style setting market risk by hedging with underlying liquidly traded assets rate derivatives Pricing models for Bermudan-style interest and options. Pricing models must be arbitrage-free, and consistent with (calibrated to) prices of actively traded underlying options. interest rate derivatives Model dynamics need be consistent with the observed dynamics of the term structure of interest rates, e.g., correlation between inte- rest rates. Moreover, valuation algorithms need be efficient: Finan- cial decisions based on derivatives pricing calculations often need to be made in seconds, rather than hours or days. In recent years, a successful class of models has appeared in the literature known as market models. This thesis extends the theory of market models, in the following ways: (i) it introduces a new, efficient, and more accurate approximate pricing technique, (ii) it presents two new and fast algorithms for correlation-calibration, (iii) it develops new models that enable efficient calibration for a whole new range of deriva- tives, such as fixed-maturity Bermudan swaptions, and (iv) it presents novel empirical comparisons of the performance of existing calibra- tion techniques and models, in terms of reduction of risk. -
Exotic Interest-Rate Options
Exotic interest-rate options Marco Marchioro www.marchioro.org November 10th, 2012 Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 1 Lecture Summary • Exotic caps, floors, and swaptions • Swaps with exotic floating-rate legs • No-arbitrage methods (commodity example) • Numeraires and pricing formulas • stochastic differential equations (SDEs) • Partial differential equations (PDEs) • Feynman-Kac formula • Numerical methods: analytical approximations Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 2 Common exotic interest-rate options There are all sorts of exotic interest-rate options. The least exotic, i.e. commonly traded, types are • Caps and floors with a digital payoff • Caps and floors with barriers • Bermuda and American Swaptions Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 3 Caps and floors with a digital payoff A vanilla Cap has caplets with payoff Payoff CapletV = NT (6m; 9m) max [(3m-Libor − K); 0] (1) A digital Cap has caplets with payoff 8 > NT (6m; 9m) R for 3m-Libor ≥ K Payoff < CapletD = (2) :> 0 for 3m-Libor < K Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 4 Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 5 Caps and floors with barriers A barrier Cap has caplets with payoff Payoff CapletV = NT (6m; 9m) max [(3m-Libor − K); 0] (3) • Knock-in: paid if 3m-Libor touches a barrier rknock-in • Knock-out: paid if 3m-Libor does not reach rknock-out Discrete barriers are checked at certain given barrier dates Continuous barriers are checked on each daily Libor fixing Digital payoffs are also available. -
Franklin Floating Rate Daily Access Fund Summary Prospectus
SUMMARY PROSPECTUS FRANKLIN FLOATING RATE DAILY ACCESS FUND Franklin Investors Securities Trust March 1, 2021 Class A Class C Class R6 Advisor Class FAFRX FCFRX FFRDX FDAAX Before you invest, you may want to review the Fund’s prospectus, which contains more information about the Fund and its risks. You can find the Fund’s prospectus, statement of additional information, reports to shareholders and other information about the Fund online at www.franklintempleton.com/prospectus. You can also get this information at no cost by calling (800) DIAL BEN/342-5236 or by sending an e-mail request to [email protected]. The Fund’s prospectus and statement of additional information, both dated March 1, 2021, as may be supplemented, are all incorporated by reference into this Summary Prospectus. Click to view the fund’s prospectus or statement of additional information. FRANKLIN FLOATING RATE DAILY ACCESS FUND SUMMARY PROSPECTUS Investment Goal High level of current income. A secondary goal is preservation of capital. Fees and Expenses of the Fund These tables describe the fees and expenses that you may pay if you buy and hold shares of the Fund. You may qualify for sales charge discounts in Class A if you and your family invest, or agree to invest in the future, at least $100,000 in Franklin Templeton funds. More information about these and other discounts is available from your financial professional and under “Your Account” on page 149 in the Fund’s Prospectus and under “Buying and Selling Shares” on page 89 of the Fund’s Statement of Additional Information. -
Convexity Adjustment for Constant Maturity Swaps and Libor-In-Arrears Basis Swaps12
TMG Financial Products Inc. 475 Steamboat Road Greenwich, CT 06830 Thomas S. Coleman 15 November 1995 VP, Risk Management, 203-861-8993 revised 30 August 1996 CONVEXITY ADJUSTMENT FOR CONSTANT MATURITY SWAPS AND LIBOR-IN-ARREARS BASIS SWAPS12 INTRODUCTION The Constant Maturity Swap or Treasury (CMS or CMT) market is large and active. The difficulty of evaluating the implicit convexity cost, however, makes the markets more opaque than would otherwise be the case. This note lays out a practical method for calculating the value of the convexity adjustment for the linear CMS/CMT and LIBOR-in-arrears payments. Both CMT/CMS and LIBOR-in-arrears swaps share the characteristic that the payment on one side of the swap is linear with respect to its index while the offsetting hedge is convex. The linearity of the payment (relative to the convex hedges) imposes a cost that leads to the "convexity adjustment" made to the linear payment. The basis of the approach used here is to 1. Find for each reset date the equivalent martingale measure (forward measure using a zero bond as numeraire) which makes the PV of a traded swap equal to its market value. In practical terms, this reduces to finding the "adjusted mean" of the rate distribution as of the reset date. For log-normally distributed rates, there are approximations which make this fast. 2. The same forward measure is then used to calculate the PV of the CMS/CMT swap or the LIBOR-in-arrears payment (which is not actively traded). This PV incorporates the convexity cost of the linear payment relative to its (traded) convex hedge. -
The Efficient Pricing of CMS and CMS Spread Derivatives
Delft University of Technology Faculty of Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics The efficient pricing of CMS and CMS spread derivatives A thesis submitted to the Delft Institute of Applied Mathematics in partial fulfillment of the requirements for the degree MASTER OF SCIENCE in APPLIED MATHEMATICS by Sebastiaan Louis Cornelis Borst Delft, the Netherlands September 2014 Copyright c 2014 by Sebastiaan Borst. All rights reserved. MSc THESIS APPLIED MATHEMATICS \The efficient pricing of CMS and CMS spread derivatives" Sebastiaan Louis Cornelis Borst Delft University of Technology Daily supervisor Responsible professor Dr. N. Borovykh Prof. dr. ir. C.W. Oosterlee Other thesis committee members Dr. P. Cirillo September 2014 Delft, the Netherlands Abstract Two popular products on the interest rate market are Constant Maturity Swap (CMS) deriva- tives and CMS spread derivatives. This thesis focusses on the efficient pricing of CMS and CMS spread derivatives, in particular the pricing of CMS and CMS spread options. The notional values for these products are usually quite large, so even small errors when pricing these products can lead to substantial losses. Therefore, the pricing of these products has to be accurate. It is possible to use sophisticated models (e.g. Libor Market Model) to price these products, however the downside is that these models generally have high computational costs; they are not very efficient. To efficiently price CMS options the Terminal Swap Rate (TSR) approach can be used. From this approach TSR models are obtained, we will consider four different TSR models. Two of these TSR models are established in the literature, the other two TSR models are developed in this thesis. -
1 Overview of Derivatives
1 Overview of Derivatives A financial derivative is usually defined as an instrument whose value is derived from some underlying cash market instrument. Familiar examples include • options to { buy (\call options") or { sell (\put options") a specified security or commodity at a specified price on a specified date, and • contracts such as { futures or { options on equity indices such Standard & Poor's 500. Newer examples include structured notes, which are securities whose interest or principal payments depend on market conditions, such as floating rate notes and inverse floaters. Swaps of various kinds are also derivatives. Various kinds of derivative are described by Hull, with both details of how their markets operate and the theory of pricing. 1.1 Exchange-Traded versus Over-the-Counter A significant distinction is that between exchange-traded and over-the-counter (\OTC") derivatives. Derivatives that are traded on an exchange are stan- dardized to promote liquidity. They are \marked to market" as of the close of business every day, and the holder's brokerage account is credited or deb- ited with the day's change in value. The holder is required to keep cash or securities in the account sufficient to cover the next day's possible losses with a very high level of probability; this margin protects the other partici- pants against default by the holder of an \out of the money" position. Each instrument is a contract between the holder and the exchange. The OTC market consists of an informal system of dealers linked by telephone, and allows transactions to be customized to meet the precise needs 1 of the dealers' clients.