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GLASSERMAN, PAUL. 2004. Monte Carlo Methods in Financial Engineering: Applications of Mathematics, Stochastic Modelling and Applied Probability. Springer-Verlag, New York. 596 pp. $69.95.
In recent years, researchers have published many papers on financial mathematics. Many of these papers concern specific questions about stochastic processes and are directed towards theoreticians in probability theory rather than the finance audience. Several monographs summarize the results in the field for experts and students in stochastic processes. Springer-Verlag has published three books (Karatzas and Shreve 1998, Musiela and Rutkowski 1997, Niederreiter 1992) in the same series as Glasserman's book that are intended for narrower audiences.
Glasserman's book consists of nine chapters and three appendices. In the first chapter, Glasserman introduces the principles of Monte Carlo techniques and of derivative pricing. The main idea is to formulate a problem of derivative pricing as an integration problem. Integration problems can be solved using Monte Carlo techniques. Two subsequent chapters concern methods of generating random numbers, random variables, and sample paths of stochastic processes. The chapter on generating random numbers and random variables contains the standard material normally covered in a textbook on Monte Carlo methods. In the chapter on generating sample paths, the author considers stochastic processes suitable as models for financial engineering, for example, Brownian and geometric Brownian motions, square-root diffusion, and processes with jumps. He discusses the mathematical properties of the models and their economic sense, enabling readers with limited knowledge of mathematical finance to understand the context.
Although Monte Carlo techniques...