Interest rate modeling : theory and practice

著者

    • Wu, Lixin

書誌事項

Interest rate modeling : theory and practice

Lixin Wu

（Chapman & Hall/CRC financial mathematics series）

CRC Press, c2009

  • : hbk

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注記

"A Chapman & Hall book"

Includes bibliographical references (p. 319-325) and index

内容説明・目次

内容説明

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.

目次

The Basics of Stochastic Calculus Brownian Motion Stochastic Integrals Stochastic Differentials and Ito's Lemma Multi-Factor Extensions Martingales The 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 Notes Interest 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 Model Lognormal Model: The Starting Point The HJM Model Special Cases of the HJM Model Estimating the HJM Model from Yield Data A Case Study with a Two-Factor Model Monte Carlo Implementations Forward Prices Forward Measure Black's Formula for Call and Put Options Numeraires and Changes of Measure Notes Short-Rate Models and Lattice Implementation From Short-Rate Models to Forward-Rate Models General Markovian Models Binomial Trees of Interest Rates A General Tree-Building Procedure The LIBOR Market Model LIBOR Market Instruments The LIBOR Market Model Pricing of Caps and Floors Pricing of Swaptions Specifications of the LIBOR Market Model Monte Carlo Simulation Method Calibration of LIBOR Market Model Implied Cap and Caplet Volatilities Calibrating the LIBOR Market Model to Caps Calibration to Caps, Swaptions, and Input Correlations Calibration Methodologies Sensitivity with Respect to the Input Prices Notes Volatility and Correlation Adjustments Adjustment due to Correlations Adjustment due to Convexity Timing Adjustment Quanto Derivatives Notes Affine Term Structure Models An Exposition with One-Factor Models Analytical Solution of Riccarti Equations Pricing Options on Coupon Bonds Distributional Properties of Square-Root Processes Multi-Factor Models Swaption Pricing under ATSMs Notes References Index

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