01 / Reading Guide
Reading Guide
Citation
Rebonato, R. (2003). Modern pricing of interest-rate derivatives: The LIBOR market model and beyond. Princeton University Press.
Chapter Summary
Introduction
States the aim of the book: a satisfactory way to price a wide range of interest-rate derivatives with the LIBOR market model. The author acknowledges that implementations differ and explains his preferred version of the model and his calibration philosophy.
Part I: The Structure of the LIBOR Market Model
Chapters 1–2: Putting the Modern Pricing Approach in Perspective; The Mathematical and Financial Set-up
A historical overview of interest-rate derivative modelling and the arrival of the market model, with attention to no-arbitrage conditions and the role of volatilities and correlations. Chapter 2 lays out the modelling framework, the securities market and the valuation of plain-vanilla instruments.
Chapters 3–4: Describing the Dynamics of Forward Rates; Characterizing and Valuing Complex LIBOR Products
The dynamics of forward rates in the modern pricing approach, equivalent descriptions and generalizations, including the swap-rate-based model. Chapter 4 describes the complex products that the model can handle and includes a case study of pricing in a multi-factor world.
Chapter 5: Determining the No-Arbitrage Drifts of Forward Rates
Derives the drift terms the no-arbitrage condition requires, expresses them in market-related quantities, and discusses approximations.
Part II: The Inputs to the General Framework
Chapter 6: Instantaneous Volatilities
Why instantaneous volatility functions matter, general results, and specific functional forms with their financial interpretation.
Chapter 7: Specifying the Instantaneous Correlation Function
General considerations, empirical evidence on correlations, and proposed functional forms with a discussion of their plausibility.
Part III: Calibration of the LIBOR Market Model
Chapter 8: Fitting the Instantaneous Volatility Functions
The general calibration philosophy, with approaches to fitting the caplet market and swaption matrices.
Chapter 9: Simultaneous Calibration to Market Caplet Prices and to an Exogenous Correlation Matrix
A procedure for recovering a target correlation matrix while matching caplet prices, with results.
Chapter 10: Calibrating a Forward-Rate-Based LIBOR Market Model to Swaption Prices
Why forward and swap-rate dynamics need joint description, and computational results on European swaptions and calibration methods.
Part IV: Beyond the Standard Approach: Accounting for Smiles
Chapter 11: Extending the Standard Approach - 1: CEV and Displaced Diffusion
The practical and conceptual consequences of non-flat volatility smiles, and ways of accommodating them with CEV and displaced diffusion.
Chapters 12–13: Extending the Standard Approach - II: Stochastic Instantaneous Volatilities; A Joint Empirical and Theoretical Analysis of the Stochastic-Volatility LIBOR Market Model
The stochastic-volatility extension, with numerical techniques and results, and an analysis combining empirical evidence and theory on how well the model reproduces a stochastic term structure of volatilities. A bibliography and index close the book.
Key Concepts
Part I
- LIBOR market model: a model whose state variables are the forward LIBOR rates that underlie caps and swaptions.
- No-arbitrage drift: the drift of each forward rate that follows from its volatility and from the chosen numeraire.
- Complex LIBOR products: derivatives whose pricing requires the joint dynamics of many forward rates.
Part II
- Instantaneous volatility function: the time-dependent volatility of each forward rate.
- Instantaneous correlation function: the correlation among forward rates of different maturities.
Parts III–IV
- Calibration: fitting the model to caplet and swaption prices, with attention to whether simultaneous fitting is financially justified.
- Implied volatility smile: why prices at different strikes need more than a flat volatility.
- CEV and displaced diffusion: first extensions to account for smiles.
- Stochastic volatility LIBOR market model: the extension with stochastic instantaneous volatilities.
Critical Analysis
Strengths
- Insight from both sides of the market. The publisher's summary says the author draws on academic and professional experience to bring together what theory and trading each offer, and the book gives its attention to the financial justification as well as the mathematics.
- Calibration is treated in detail. Three chapters address fitting to caplet and swaption prices and to a target correlation matrix, and the summary highlights the question of whether simultaneous fitting to several observables is advisable, with attention to market incompleteness.
- A sustained treatment of the smile. Part IV develops an original stochastic-volatility, displaced-diffusion extension and examines it both computationally and empirically.
- Clear structure. The four parts follow the logic of the problem: structure, inputs, calibration, then refinements.
Limitations
- A specialist monograph. The book is described as essential reading for quantitative researchers, sophisticated derivatives practitioners and finance students; it assumes familiarity with arbitrage pricing, stochastic calculus and standard interest rate models.
- Built around the author's approach. Much of the book develops the author's own extension of the model, so readers wanting a neutral survey of competing frameworks need another text.
- Dated reference rates. The book predates the move away from LIBOR as a benchmark, so its LIBOR-based setting should be read as a model of forward rates in general.
Where It Fits in the Course
Within the asset pricing and derivatives list this is the specialist interest-rate derivatives monograph, to be read after the basics. Hull's Options, Futures, and Other Derivatives gives products and market background; Veronesi's Fixed Income Securities and Tuckman and Serrat's text cover bonds, term structure and swaps first. For the mathematics, Björk's Arbitrage Theory in Continuous Time, Bingham and Kiesel's Risk-Neutral Valuation and Musiela and Rutkowski's Martingale Methods in Financial Modelling are the likeliest prior reading, the last also treating market LIBOR models in a chapter of its own.
Glasserman's Monte Carlo Methods in Financial Engineering is the natural companion for implementing the simulation-based pricing that the LIBOR market model usually needs.
How to Use This Book
The book is for graduate students, quantitative analysts and researchers who already know term structure modelling and want to see how a market model is built, calibrated and extended.
A sensible reading plan is to read the Introduction and Part I in order, then Chapters 6 and 7 for the inputs, and then Part III for calibration. Part IV is the most specialist and can be read last, or selectively by readers whose focus is volatility smiles. Readers who need only the standard model can stop after Part III. Rebuild the volatility and correlation parameterisations in code to follow the calibration chapters.