Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives

Citation

Bingham, N. H., & Kiesel, R. (2004). Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives (2nd ed.). Springer.

Chapter Summary

The second edition has nine chapters and one appendix, in about 440 pages including the appendix and index. The chapter titles show a deliberate order: a background chapter on derivatives and one on probability, then a pair of chapters for discrete time (stochastic processes, then mathematical finance), a matching pair for continuous time, and three further chapters on incomplete markets, interest rates and credit risk. Following the success of the first edition, the authors thoroughly revised the whole book for this edition; the publisher says the chapters on incomplete markets and interest rate theory were updated and extended, that the credit risk chapter is new, and that there is new material on Lévy finance.

Chapter 1: Derivative Background

The opening chapter supplies the financial vocabulary and setting for the rest of the book (pages 1–27).

Chapter 2: Probability Background

This chapter, the longest of the preparatory material at 45 pages, collects the probability that the later chapters require.

Chapter 3: Stochastic Processes in Discrete Time

A short chapter (pages 75–99) that develops the stochastic processes needed for the discrete-time pricing theory.

Chapter 4: Mathematical Finance in Discrete Time

The first chapter of pricing theory proper, about fifty pages, which applies the preceding material to financial models in discrete time.

Chapter 5: Stochastic Processes in Continuous Time

The longest chapter in the book at roughly 75 pages, it is the continuous-time counterpart of Chapter 3.

Chapter 6: Mathematical Finance in Continuous Time

The continuous-time counterpart of Chapter 4 (pages 229–288), where the pricing theory is taken to continuous-time models.

Chapter 7: Incomplete Markets

A chapter the publisher says has been updated and extended for this edition, and which includes new material on Lévy-based models in incomplete markets.

Chapter 8: Interest Rate Theory

Also updated and extended in this edition, this chapter treats interest-rate modelling in the setting built up by the preceding chapters.

Chapter 9: Credit Risk

A chapter new to the second edition, on what the publisher calls the important and growing area of credit risk.

Appendix A: Hilbert Space

A reference appendix (from page 409) closes the book before the index.

Key Concepts

Chapters 1–2

• Risk-neutral valuation: the principle in the title, which the publisher describes as a major tool for pricing and hedging derivatives since the early 1980s.
• Derivatives: the instruments whose pricing and hedging the book addresses.

Chapters 3–6

• Stochastic processes in discrete and continuous time: the probabilistic tools introduced in each setting before the finance is built on them.
• Mathematical finance: pricing theory developed first in discrete time and then in continuous time.

Chapters 7–9

• Incomplete markets: markets in which not every claim can be hedged, and the pricing questions that arise.
• Interest rate theory and credit risk: the two applications developed in the last chapters.
• Lévy processes: infinite divisibility and Lévy-based models, new in this edition.

Critical Analysis

Strengths

• Gradual construction. Each continuous-time chapter has a discrete-time counterpart, so a reader can see the main ideas in the simpler setting before meeting the technical machinery of continuous time.
• Mathematical foundations are included. Dedicated chapters on probability and on stochastic processes, plus a Hilbert space appendix, mean the book supplies much of what its own arguments need.
• A revised second edition. The edition adds credit risk and Lévy material and extends the treatments of incomplete markets and interest rates, so it reaches beyond the basic pricing models.
• Lecturer support. The publisher notes that exercises, solutions to exercises and lecture slides are available on the web for lecturers.

Limitations

• Mathematical level. Three of the first six chapters (probability, and stochastic processes in discrete and continuous time) are preparatory mathematics, which signals a mathematical treatment; readers will need a solid mathematical background to follow it.
• Not a practitioner's manual. The title and chapter list are organised around pricing theory; hedging in practice, trading and the institutions of derivatives markets are not chapters of their own.
• Dated in places. Published in 2004, it predates later developments in the field.
• Brief later chapters. Interest rate theory runs to about 48 pages and credit risk to about 34, so each is an introduction and not a full treatment.

Where It Fits in the Course

Within the course, Bodie, Kane and Marcus's Investments is a graduate-level text on portfolio theory, equilibrium pricing, fixed income and derivatives, and Hunt et al.'s Financial Derivatives in Theory and Practice is a graduate-level study of derivatives that combines theory with pricing and hedging. Bingham and Kiesel are the more mathematically organised of these: their chapter titles show the probability and stochastic process theory for derivative pricing built up first, in discrete and then continuous time.

For the neighbouring topics, Duffie et al.'s Credit Risk: Pricing, Measurement, and Management and the fixed-income texts by Tuckman et al., Veronesi and Sundaresan extend what Chapters 8 and 9 introduce, and Mishkin and Eakins' Financial Markets and Institutions and Jordan et al.'s Fundamentals of Investments are the gentler background in how markets work. Read an investments text first, then this book as the mathematical core of derivative pricing.

How to Use This Book

The book suits graduate students in mathematical finance, financial engineering or quantitative finance, and mathematicians moving into finance.

• Core: Chapters 1 to 6, taken in order. Readers who already have the probability and stochastic process background can skim Chapters 2, 3 and 5 and read the finance chapters, 4 and 6, closely.
• Extension: Chapters 7 to 9 are chosen by interest: incomplete markets for the more general theory, interest rates for term-structure modelling, credit risk for default.
• Appendix: consult the Hilbert space appendix when an argument calls for it.
• Practice: do the exercises, and check whether your instructor can provide the solutions the publisher makes available to lecturers.