Interest Rate Modeling

Theory and Practice

Inbunden, Engelska, 2009

Av Lixin Wu

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Containing many results that are new or exist only in recent research articles, Interest Rate Modeling: Theory and Practice portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods.The text begins with the mathematical foundations, including Ito’s calculus and the martingale representation theorem. It then introduces bonds and bond yields, followed by the Heath–Jarrow–Morton (HJM) model, which is the framework for no-arbitrage pricing models. The next chapter focuses on when the HJM model implies a Markovian short-rate model and discusses the construction and calibration of short-rate lattice models. In the chapter on the LIBOR market model, the author presents the simplest yet most robust formula for swaption pricing in the literature. He goes on to address model calibration, an important aspect of model applications in the markets; industrial issues; and the class of affine term structure models for interest rates.Taking a top-down approach, Interest Rate Modeling provides readers with a clear picture of this important subject by not overwhelming them with too many specific models. The text captures the interdisciplinary nature of the field and shows readers what it takes to be a competent quant in today’s market.This book can be adopted for instructional use. For this purpose, a solutions manual is available for qualifying instructors.

Produktinformation

Utgivningsdatum2009-05-14
Mått156 x 234 x undefined mm
Vikt635 g
FormatInbunden
SpråkEngelska
SerieChapman & Hall/CRC Financial Mathematics Series
Antal sidor354
FörlagTaylor & Francis Ltd
ISBN9781420090567

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Finansiering inom Ekonomi och ledarskap

The Basics of Stochastic Calculus Brownian Motion Stochastic Integrals Stochastic Differentials and Ito’s Lemma Multi-Factor ExtensionsMartingalesThe Martingale Representation Theorem Changing Measures with Binomial Models Change of Measures under Brownian Filtration The Martingale Representation Theorem A Complete Market with Two Securities Replicating and Pricing of Contingent Claims Multi-Factor Extensions A Complete Market with Multiple Securities The Black–Scholes Formula NotesInterest Rates and Bonds Interest Rates and Fixed-Income Instruments Yields Zero-Coupon Bonds and Zero-Coupon Yields Forward Rates and Forward-Rate Agreements Yield-Based Bond Risk Management The Heath–Jarrow–Morton ModelLognormal Model: The Starting PointThe HJM ModelSpecial Cases of the HJM ModelEstimating the HJM Model from Yield Data A Case Study with a Two-Factor ModelMonte Carlo ImplementationsForward PricesForward MeasureBlack’s Formula for Call and Put Options Numeraires and Changes of MeasureNotesShort-Rate Models and Lattice ImplementationFrom Short-Rate Models to Forward-Rate Models General Markovian Models Binomial Trees of Interest Rates A General Tree-Building Procedure The LIBOR Market ModelLIBOR Market InstrumentsThe LIBOR Market ModelPricing of Caps and Floors Pricing of SwaptionsSpecifications of the LIBOR Market ModelMonte Carlo Simulation MethodCalibration of LIBOR Market ModelImplied Cap and Caplet Volatilities Calibrating the LIBOR Market Model to CapsCalibration to Caps, Swaptions, and Input Correlations Calibration MethodologiesSensitivity with Respect to the Input Prices NotesVolatility and Correlation AdjustmentsAdjustment due to CorrelationsAdjustment due to ConvexityTiming Adjustment Quanto Derivatives NotesAffine Term Structure ModelsAn Exposition with One-Factor ModelsAnalytical Solution of Riccarti Equations Pricing Options on Coupon Bonds Distributional Properties of Square-Root Processes Multi-Factor Models Swaption Pricing under ATSMsNotesReferences Index

"The book presents in a balanced way both theory and applications of interest rate modeling. …The book can serve as a textbook. It is self-contained in mathematics and presents rigorous justifications for almost all results. Many exercises are provided which often require computer implementation. To a large extent, this book can also serve as a research monograph as it contains many new results. The book shows the readers what has to be a competent quantitative analysis in financial markets."—Pavel Stoynov, Zentralblatt MATH 1173