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Andersen L.B.G., Piterbarg V.V. Interest Rate Modeling (Volumes 1, 2, 3)
Atlantic Financial Press – 2004, 1188 pages
ISBN: 0984422102, 0984422110, 0984422129

The book is organized into three volumes, five parts (plus appendix), and 26 chapters:

Part I. Foundations
Introduction to Arbitrage Pricing Theory
Finite Difference Methods
Monte Carlo Methods)
Fundamentals of Interest Rate Modelling
Fixed Income Instruments
Part II. Vanilla Models
Yield Curve Construction and Risk Management
Vanilla Models with Local Volatility
Vanilla Models with Stochastic Volatility I
Vanilla Models with Stochastic Volatility II
Part III. Term Structure Models
One-Factor Short Rate Models I
One-Factor Short Rate Models II
Multi-Factor Short Rate Models
The Quasi-Gaussian Model with Local and Stochastic Volatility
The Libor Market Model I
The Libor Market Model II
Part IV. Products
Single-Rate Vanilla Derivatives
Multi-Rate Vanilla Derivatives
Callable Libor Exotics
Bermudan Swaptions
TARNs, Volatility Swaps, and Other Derivatives
Out-of-Model Adjustments
Part V. Risk management
Fundamentals of Risk Management
Payoff Smoothing and Related Methods
Pathwise Differentiation
Importance Sampling and Control Variates
Vegas in Libor Market Models
Appendix

The three volumes of Interest Rate Modeling present a comprehensive and up-to-date treatment of techniques and models used in the pricing and risk management of fixed income securities. Written by two leading practitioners and seasoned industry veterans, this unique series combines finance theory, numerical methods, and approximation techniques to provide the reader with an integrated approach to the process of designing and implementing industrial-strength models for fixed income security valuation and hedging. Aiming to bridge the gap between advanced theoretical models and real-life trading applications, the pragmatic, yet rigorous, approach taken in this book will appeal to students, academics, and professionals working in quantitative finance.

Volume I provides the theoretical and computational foundations for the series, emphasizing the construction of efficient grid- and simulation-based methods for contingent claims pricing. Numerical methods serve an extremely important role in the text, so we develop this topic to an advanced level suitable for professional-quality model implementations. Placing this material early in the text allows us to incorporate it into our discussion of individual models in subsequent chapters. The second part of Volume I is dedicated to local-stochastic volatility modeling and to the construction of vanilla models for individual swap and Libor rates. Although the focus is eventually turned toward fixed income securities, much of the material in this volume applies to a broad capital market setting and will be of interest to anybody working in the general area of asset pricing.

Volume II is dedicated to in-depth study of term structure models of interest rates. While providing a thorough analysis of classical short rate models, the primary focus of the volume is on multi-factor stochastic volatility dynamics, in the setups of both the separable HJM and Libor market models. Implementation techniques are covered in detail, as are strategies for model parameterization and calibration to market data.

The first half of Volume III contains a detailed study of several classes of fixed income securities, ranging from simple vanilla options to highly exotic cancelable and path-dependent trades. The analysis is done in product-specific fashion, covering, among other subjects, risk characterization, calibration strategies, and valuation methods. In its second half, Volume III studies the general topic of derivative portfolio risk management, with a particular emphasis on the challenging problem of computing smooth price sensitivities to market input perturbations.
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