Interest Rate Dynamics Derivatives Pricing And Risk Management

There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc ture consistent with the initial tenn structure data.

There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc ture consistent with the initial tenn structure data.

Book and CDROM include the important topics and cutting-edge research in financial derivatives and risk management.

This book combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these models to the risk and portfolio management of interest-rate derivatives. It can also serve as a valuable textbook on financial markets for graduate and PhD students in mathematics. Interesting and comprehensive case studies illustrate the theoretical concepts.

This book presents 20 peer-reviewed chapters on current aspects of derivatives markets and derivative pricing. The contributions, written by leading researchers in the field as well as experienced authors from the financial industry, present the state of the art in: • Modeling counterparty credit risk: credit valuation adjustment, debit valuation adjustment, funding valuation adjustment, and wrong way risk. • Pricing and hedging in fixed-income markets and multi-curve interest-rate modeling. • Recent developments concerning contingent convertible bonds, the measuring of basis spreads, and the modeling of implied correlations. The recent financial crisis has cast tremendous doubts on the classical view on derivative pricing. Now, counterparty credit risk and liquidity issues are integral aspects of a prudent valuation procedure and the reference interest rates are represented by a multitude of curves according to their different periods and maturities. A panel discussion included in the book (featuring Damiano Brigo, Christian Fries, John Hull, and Daniel Sommer) on the foundations of modeling and pricing in the presence of counterparty credit risk provides intriguing insights on the debate.

Dynamic methods for interest rate risk pricing and hedging. Fixed-Income Securities provides a survey of modern methods forpricing and hedging fixed-income securities in the presence ofinterest rate risk. Modern theory of finance provides a wealth ofnew approaches to the important question of interest rate riskmanagement, and this book brings them together, in a comprehensiveand thorough treatment of the subject. Structured in an accessible manner, the authors begin by focusingon pricing and hedging certain cash flows, before moving on toconsider pricing and hedging uncertain cash flows. In addition tothe theoretical explanation, the authors provide numerousreal-world examples and applications throughout. This is the first book I have seen to carefully cover such a wideset of topics in both theoretical and applied fixed-incomemodelling, ranging from the use of market information to obtainyield curves, to the pricing and hedging of bonds and fixed-incomederivatives, to the currently active topic of defaultableyield-curve modelling. It will be particularly useful topractitioners.Darrell Duffie, Stanford University This is the most comprehensive theoretical treatment of thesubject I ve ever seen. Mark Rubinstein, Haas School of Business,University of California An excellent review of interest rate models and of the pricing andhedging principles in the fixed-income area.Oldrich Alfons Vasicek,KMV Corporation

Interest Rate Modeling for Risk Management introduces a theoretical framework - the ‘real-world’ model - that allows us to estimate the market price of interest rate risk based on practical and real life situations. The model can be briefly summarized as a process of estimating the market prices of risk through discretization of forward rates with a ‘space-state setup’ whilst considering historical data trends. The book starts with a brief explanation of interest rate stochastic analysis fundamentals before delving into standard models such as Heath-Jarrow-Morton, Hull-White and LIBOR models. The real-world model is then explained in subsequent chapters while applying different frameworks. Additionally, the book also explains some properties of the real-world model, along with the negative price tendency of the market price for risk and a positive market price for risk (with an example of this actually occurring). Readers will also find a handy appendix with proofs to complement the numerical methods explained in the book. This book is intended as a primer for practitioners in financial institutions involved in interest rate risk management. It also presents a new perspective for researchers and graduates in econometrics and finance on the study of interest rate models.

This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.

Now in its fifth edition, Derivatives and Internal Models provides a comprehensive and thorough introduction to derivative pricing, risk management and portfolio optimization, covering all relevant topics with enough hands-on, depth of detail to enable readers to develop their own pricing and risk tools. The book provides insight into modern market risk quantification methods such as variance-covariance, historical simulation, Monte Carlo, hedge ratios, etc., including time series analysis and statistical concepts such as GARCH Models or Chi-Square-distributions. It shows how optimal trading decisions can be deduced once risk has been quantified by introducing risk-adjusted performance measures and a complete presentation of modern quantitative portfolio optimization. Furthermore, all the important modern derivatives and their pricing methods are presented; from basic discounted cash flow methods to Black-Scholes, binomial trees, differential equations, finite difference schemes, Monte Carlo methods, Martingales and Numeraires, terms structure models, etc. The fifth edition of this classic finance book has been comprehensively reviewed. New chapters/content cover multicurve bootstrapping, the valuation and hedging of credit default risk that is inherently incorporated in every derivative—both of which are direct and permanent consequences of the financial crises with a large impact on our understanding of modern derivative valuation. The book will be accompanied by downloadable Excel spread sheets, which demonstrate how the theoretical concepts explained in the book can be turned into valuable algorithms and applications and will serve as an excellent starting point for the reader’s own bespoke solutions for valuation and risk management systems.

19.1. Numerical analysis and simulation techniques : an introduction to finite difference methods. 19.2. Application to European options on non-dividend paying stocks. 19.3. Valuation of American options with a composite volatility. 19.4. Simulation methods : Monte-Carlo method. ch. 20. Numerical methods and partial differential equations for European and American derivatives with complete and incomplete information. 20.1. Valuation of American calls on dividend-paying stocks. 20.2. American puts on dividend-paying stocks. 20.3. Numerical procedures in the presence of information costs : applications. 20.4. Convertible bonds. 20.5. Two-factor interest rate models and bond pricing within information uncertainty. 20.6. CBs pricing within information uncertainty -- pt. VIII. Exotic derivatives. ch. 21. Risk management : exotics and second-generation options. 21.1. Exchange options. 21.2. Forward-start options. 21.3. Pay-later options. 21.4. Simple chooser options. 21.5. Complex choosers. 21.6. Compound options. 21.7. Options on the maximum (minimum). 21.8. Extendible options. 21.9. Equity-linked foreign exchange options and quantos. 21.10. Binary barrier options. 21.11. Lookback options. ch. 22. Value at risk, credit risk, and credit derivatives. 22.1. VaR and riskmetrics : definitions and basic concepts. 22.2. Statistical and probability foundation of VaR. 22.3. A more advanced approach to VaR. 22.4. Credit valuation and the creditmetrics approach. 22.5. Default and credit-quality migration in the creditmetrics approach. 22.6. Credit-quality correlations. 22.7. Portfolio management of default risk in the Kealhofer, McQuown and Vasicek (KMV) approach. 22.8. Credit derivatives : definitions and main concepts. 22.9. The rating agencies models and the proprietary models.