Mathematical Models of Financial Derivatives

The second edition of Yue-Kuen Kwok's Mathematical Models of Financial Derivatives is a rather comprehensive collection of known facts and techniques, as well as a methodologically thought-through textbook on derivative pricing in financial markets. The book is written both for a novice who will profit from its numerous and well-conceived exercises, and a practitioner who wants to brush up on finer points of the classical pricing theory behind a specific financial product.

Starting with the very basic economic and financial notions, including a glossary-like overview of the important derivatives, the author moves to the mathematical framework and gives a short introduction to stochastic analysis both in discrete and continuous time. Although mathematical precision permeates the discrete part, heuristic arguments quickly start replacing mathematical technicalities in the proofs in continuous time and the rest of the book. While such an exposition may throw off a more rigor-demanding reader, it will certainly attract many a non-mathematician with an interest in quantitative methods in finance, but without time to spare on mathematical details. The book continues with an in-depth treatment of option pricing in the Black-Scholes-Merton-Samuelson model and continues with chapters on American and path-dependent options. After a short introduction to various numerical methods, it turns to interest-rate models and related derivative securities.

Summing up, Kwok's book is an introduction to the classical theory of derivative pricing in the spirit of Wilmott's Option Pricing, but more comprehensive and with numerous exercises. It only touches upon topics outside the Black-Scholes framework (such as transaction costs, illiquidity, stochastic volatility, jumps or market incompleteness in general). However, with 530 pages already between its covers, it would not be fair to expect a deeper treatment.

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Gordan Žitković is an assistant professor of mathematics at the University of Texas at Austin. His interests include mathematical finance, mathematical economics and optimal stochastic control.