When implementing mathematical models for pricing interest rate derivatives one must address a number of practical issues such as the choice of a satisfactory model, the calibration to market data, the implementation of efficient routines, and so on. This book explains how models work and how to implement them for concrete pricing.

The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, a discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced.

The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach.

The fast-growing interest for hybrid products has led to a new chapter, with a special focus devoted to the pricing of convertible bonds and inflation-linked derivatives.

Klappentext

The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced.

The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach.

Examples of calibrations to real market data are now considered.

The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives.

The three final new chapters of this second edition are devoted to credit.

Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.

Inhalt

I. Models: Theory and Implementation.- 1. Definitions and Notation.- 2. No-Arbitrage Pricing and Numeraire Change.- 3. One-factor short-rate models.- 4. Two-Factor Short-Rate Models.- 5. The Heath-Jarrow-Morton (HJM) Framework.- 6. The LIBOR and Swap Market Models (LFM and LSM).- 7. Cases of Calibration of the LIBOR Market Model.- 8. Monte Carlo Tests for LFM Analytical Approximations.- 9. Other Interest-Rate Models.- II. Pricing Derivatives in Practice.- 10. Pricing Derivatives on a Single Interest-Rate Curve.- 11. Pricing Derivatives on Two Interest-Rate Curves.- 12. Pricing Equity Derivatives under Stochastic Rates.- III. Appendices.- A. A Crash Introduction to Stochastic Differential Equations.- B. A Useful Calculation.- C. Approximating Diffusions with Trees.- D. Talking to the Traders.- References.