Financial Derivatives in Theory and Practice

Citation

Hunt, P. J., & Kennedy, J. E. (2004). Financial Derivatives in Theory and Practice (Revised ed.). John Wiley & Sons.

Chapter Summary

The revised edition has twenty chapters in two parts, three short appendices and an index (about 440 pages). Part I, Theory, covers the mathematics of arbitrage pricing; Part II, Practice, covers the modelling of interest-rate derivatives as the authors met it in the London market. The authors say the two parts can be read independently apart from cross-references for notation. Two short "Orientation" sections in Part II introduce the groups of exotic products priced there. The revised edition differs from the 2000 original only by a new final chapter of exercises with solutions and corrections of errors.

Chapter 1: Single-Period Option Pricing

Introduces replication and arbitrage in an economy with one time step and finitely many states. It treats pricing, the conditions for no arbitrage, completeness, the probabilistic formulation with pricing kernels and numeraires, and a two-period example. The preface identifies this chapter and Chapter 7 as the primary development of the finance theory.

Chapters 2–6: Brownian Motion; Martingales; Stochastic Integration; Girsanov and Martingale Representation; Stochastic Differential Equations

The stochastic-calculus background, gathered so that these chapters can stand alone as an introduction. Chapter 2 defines Brownian motion and covers the strong Markov property and the reflection principle. Chapter 3 treats martingales, stopping times, quadratic variation, local martingales and semimartingales, and the Doob–Meyer decomposition. Chapter 4 builds the stochastic integral (the L2 theory, extension by localization) and Itô's formula. Chapter 5 covers equivalent measures, Girsanov's theorem and the martingale representation theorem. Chapter 6 treats stochastic differential equations: weak and strong solutions, existence and uniqueness for Lipschitz coefficients, and the strong Markov property.

Chapter 7: Option Pricing in Continuous Time

The full continuous-time theory. After asset price processes and self-financing strategies, it prices European options both as the solution of a PDE and through an equivalent martingale measure, then develops units and numeraires, arbitrage and admissible strategies, completeness and pricing kernels, and extensions such as general payout schedules and an infinite horizon. The preface notes that the emphasis on numeraires and the choice of the filtration generated by the assets are slightly non-standard.

Chapter 8: Dynamic Term Structure Models

The last chapter of Part I is specific to interest rates. It starts from an economy of pure discount bonds and shows several ways to specify a term-structure model (pricing kernel and numeraire approaches, short-rate models, Heath–Jarrow–Morton models and Flesaker–Hughston models) and how they relate mathematically.

Chapters 9–12: Modelling in Practice; Basic Instruments and Terminology; Pricing Standard Market Derivatives; Futures Contracts

Part II opens with the issues a practitioner faces when choosing a model: the real world is not a martingale measure, product-based modelling, and local versus global calibration. Chapters 10 and 11 introduce deposits, forward rate agreements, swaps and zero-coupon bonds, then price caps, floors, vanilla and digital options and swaptions. Chapter 12 defines futures contracts, characterizes the futures price process under discrete and continuous resettlement, and relates futures to forwards.

Chapters 13–16: Terminal Swap-Rate Models; Convexity Corrections; Implied Interest Rate Pricing Models; Multi-Currency Terminal Swap-Rate Models

The European-product block, preceded by an orientation section. The authors present a modelling approach built on swap rates at a terminal date, with exponential, geometric and linear examples and a discussion of arbitrage-free properties. Chapter 14 applies it to convexity-related products such as constant maturity swaps and LIBOR-in-arrears swaps; Chapter 15 implies the model from market prices and addresses irregular swaptions; Chapter 16 extends the framework to several currencies, with spread options and cross-currency swaptions.

Chapters 17–19: Short-Rate Models; Market Models; Markov-Functional Modelling

The path-dependent and Bermudan block, also preceded by an orientation section. Chapter 17 introduces short-rate models, concentrating on Vasicek–Hull–White, with parameter fitting and a tree algorithm for Bermudan swaptions. Chapter 18 gives LIBOR and swap-based market models. Chapter 19 presents Markov-functional models, the authors' own work, which fit liquid option prices like market models but are efficient to implement.

Chapter 20: Exercises and Solutions

About 44 pages of exercises with worked solutions, added in the revised edition. Many are variants of problems set on the University of Warwick M.Sc. in Mathematical Finance and provide drill in routine interest-rate calculations. Appendices cover the usual conditions, L2 spaces and Gaussian calculations.

Key Concepts

Part I: Theory (Chapters 1–8)

• Replication and arbitrage: pricing a derivative as the cost of a portfolio that reproduces its payoff, valid only if no arbitrage exists.
• Pricing kernels, numeraires and equivalent martingale measures: the devices linking prices to expectations.
• Completeness: whether every claim can be replicated.
• Stochastic integral and Itô's formula: the calculus on which continuous-time pricing rests.
• Girsanov's theorem and martingale representation: change of measure and representation of martingales.
• Term-structure specifications: short-rate, HJM and Flesaker–Hughston models.

Part II: Practice (Chapters 9–20)

• Calibration: local versus global fitting of a model to market prices.
• Swaptions, caps and floors: the standard interest-rate options.
• Terminal swap-rate models and convexity corrections: pricing European and convexity-related products.
• Vasicek–Hull–White and market models: short-rate and LIBOR/swap models for Bermudan and path-dependent products.
• Markov-functional models: models fitted to liquid prices and implementable efficiently.

Critical Analysis

Strengths

• Two parts that can be used separately. The preface states that, apart from notation, each part can be read independently, and that a reader with a solid stochastic-calculus background could learn most of the pricing theory from Chapters 1 and 7 alone.
• Self-contained stochastic calculus. Chapters 2–6 collect only the results relevant to finance and are meant to be read as an accessible introduction in their own right.
• Practitioner perspective. The authors say Part II reflects their involvement in product development in the London interest-rate derivative market, and it moves from basic instruments to Bermudan products in increasing complexity.
• Exercises with solutions. The added Chapter 20 makes the book usable as a course text; many exercises are variants of problems set to Warwick M.Sc. students.

Limitations

• Interest-rate focus. Part II is limited to interest-rate derivatives, and Part I treats continuous asset price processes only. The authors list as omissions jumps, equilibrium theory and optimal control, the theory behind American option pricing.
• Dated in modelling. The revised-edition preface acknowledges that market models and Markov-functional models developed further after the original text and that the revised edition does not cover these advances, pointing to Rebonato (2002) and Bennett and Kennedy (2004) instead.
• Demanding mathematics. Chapters 3–6 are technical (martingales in L2, localization, existence and uniqueness proofs), and the book is written for mathematically trained readers.

Where It Fits in the Course

This is a graduate-level text for readers who want the mathematics of derivative pricing and an interest-rate modelling perspective in one volume. Bodie, Kane and Marcus's Investments and Mishkin and Eakins's Financial Markets and Institutions give the institutional and conceptual background without this mathematics. Bingham and Kiesel's Risk-Neutral Valuation is the closest relative, a mathematical treatment of risk-neutral pricing, while Hunt and Kennedy concentrate on interest rates and practical calibration.

The fixed income books (Tuckman and Serrat, Veronesi, Sundaresan) are the natural companions to Part II: they cover instruments, conventions and market institutions at greater length, and Veronesi's Part III builds some of the same continuous-time models more gently. Duffie and Singleton's Credit Risk applies the same pricing machinery to default.

How to Use This Book

The book suits graduate students in mathematical finance and quantitative practitioners comfortable with probability and calculus; the authors aim at both mathematical practitioners and academic mathematicians.

• Fast route to the theory: Chapter 1, then Chapter 7, consulting Chapters 2–6 as needed.
• Full theory course: Chapters 1–8 in order, with Chapter 8 for interest-rate models.
• Practice course: Chapters 9–12 for instruments and standard pricing, then Chapters 13–16 (European) and 17–19 (Bermudan and path-dependent); the two orientation sections explain how the chapters are grouped.
• Exercises: work Chapter 20 alongside the matching chapters, using the solutions to check routine calculations.