Book

Interest Rate Models - Theory and Practice, with Smile, Inflation, and Credit - Brigo, Mercurio

A rigorous explanation of how interest rate models work in theory, suggesting how to use them for concrete pricing. The second 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 several new chapters. 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 new chapters. 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.


  • Level: Advanced
  • Major Topics: T23, T21, T22, T24, T32
  • Minor Topics: T11, T12, T31, T33

Resources

Online Resources

Sample chapter

Table of Contents

Part I. Basic Definitions and No Arbitrage
1. Definitions and Notation
2. No-Arbitrage Pricing and Numeraire Change

Part II. From Short Rate Models to HJM
3. One-factor short-rate models
4. Two-Factor Short-Rate Models
5. The Heath-Jarrow-Morton (HJM) Framework

Part III. Market Models
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

Part IV. The Volatility Smile
9. Including the Smile in the LFM
10. Local-Volatility Models
11. Stochastic-Volatility Models
12. Uncertain-Parameter Models

Part V. Examples of Market Payoffs
13. Pricing Derivatives on a Single Interest-Rate Curve
14. Pricing Derivatives on Two Interest-Rate Curves

Part VI. Inflation
15. Pricing of Inflation-Indexed Derivatives
16. Inflation-Indexed Swaps
17. Inflation-Indexed Caplets/Floorlets
18. Calibration to market data
19. Introducing Stochastic Volatility
20. Pricing Hybrids with an Inflation Component

Part VII. Credit
21. Introduction and Pricing under Counterparty Risk
22. Intensity Models
23. CDS Options Market Models

Part VIII. Appendices
A. Other Interest-Rate Models
B. Pricing Equity Derivatives under Stochastic Rates
C. A Crash Intro to Stochastic Diferential Equations and Poisson Processes
D. A Useful Calculation
E. A Second Useful Calculation
F. Approximating Difusions with Trees
G. Trivia and Frequently Asked Questions
H. Talking to the Traders…read more