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Monte Carlo methods in finanical engineering

Since the advent of computers in financial institutions, Monte Carlo methods have come to play an essential role in simulating market scenarios for risk management and in the pricing of derivative securities. In turn, applications of Monte Carlo simulations in finance have led to interesting problems which have stimulated new developments in the field. This new book, written by an active contributor to the field of Monte Carlo methods in finance, summarizes this ongoing interaction between theory and practice in a way that is readily accessible to graduate students and practitioners in quantitative finance. The book is as self-contained as possible: basic notions on Monte Carlo simulation and option pricing are recalled in the first chapter and the second chapter explains how random number generators are designed. Chapter 3 explains how to generate sample paths for some commonly used stochastic models: multifactor Gaussian models, square root diffusions, diffusions with Poisson jumps, some examples of Lévy processes and the LIBOR market model. Instead of giving a general result and leaving the reader on his own, the author treats each example with a fair amount of detail. Chapter 4, which is the longest and probably the best chapter in the book, discusses variance reduction techniques. Variance reduction is what makes all the difference between a basic Monte Carlo simulation and a state-of-the-art algorithm incorporating the tricks of the trade. Apart from classical topics such as control variates, stratified sampling and importance sampling, the author (briefly) discusses more advanced topics such as the Weighted Monte Carlo method of Avellaneda et al, viewing it as a variance reduction method. While computation of prices as expectations are standard applications of the Monte Carlo methods, two other issues in finance have turned out to be more challenging to solve using Monte Carlo simulation: the computation of sensitivities (‘Greeks’) and the pricing of American options, which involves the maximization of conditional expectations. Chapter 7 deals with the computation of sensitivities using finite differences, pathwise derivatives and the likelihood ratio method. More advanced methods based on integration by parts (‘Malliavin calculus’) are only briefly mentioned in the conclusion to this chapter. Chapter 8 deals with the (Monte Carlo) pricing of American options, an evolving research topic in which Paul Glasserman has been an active contributor. The author has succeeded in summarizing in 60 pages a survey of various approaches: parametric methods, quantization methods, the (Broadie–Glasserman) stochastic mesh method, regressionbased methods of CarrièreLongstaff–Schwartz and duality methods (Haugh–Kogan, Rogers). The presentation is somewhat biased towards the Broadie–Glasserman approach (which is understandable!), whereas the Carrière–Longstaff– Schwartz regression method seems to be the most popular one among practitioners. One regrets the absence of a systematic comparison between these various methods in terms of numerical performance, but the chapter explains their interrelations, at least from a theoretical point of view. While most texts on Monte Carlo methods in finance have exclusively focused on option pricing, simulation of extreme events in view of VaR computation constitute another important application of Monte Carlo simulation. Chapter 9 deals with this topic and presents some importance sampling methods for simulating tail events, which turn out to be especially useful when simulating joint default events in credit risk models. A crash course on credit risk modeling is included in the chapter. The book is not written in a theorem–proof format but using an explanatory approach which I found quite pleasant, with lots of examples illustrating the results. This format seems suitable for students of financial engineering. The level of