Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers. It is an advanced book. Stochastic integrals abound, although measure theory plays no significant role. You will want to have prior knowledge of both the Monte Carlo method and financial engineering. If you do, you will find the book to be a goldmine.

The subject is covered broadly and in a systematic manner. Chapter 1 is an introduction and Chapter 2 discusses pseudorandom number and variate generation. Neither is special. Things start to get interesting in Chapter 3, which covers the generation of sample paths, starting with Brownian motion and proceeding along to the HJM and Libor market model. The discussion is simultaneously sophisticated and practical. Glasserman builds up concepts nicely. For example, he introduces the Brownian bridge in the simple case of one-dimensional Brownian motion and then extends it as he considers more elaborate models.

Chapter 3 segues seamlessly into Chapter 4, which discusses variance reduction. Standard techniques—control variates, stratified sampling, importance sampling, etc.—are all discussed in the context of financial engineering. The discussions are at the level of an advanced text on the Monte Carlo method. They are deep and address important practical issues. For example, Glasserman devotes 20 pages to control variates. He explores the use of underliers as controls. He considers an (easily priced) geometric Asian option as a control for pricing an arithmetic Asian. Hedging portfolios are also pressed into service as controls. Glasserman then goes on to explore the use of multiple controls, biases, the implementation of control variates within a weighted Monte Carlo analysis, controls that are incorporated into a Monte Carlo estimator in a non-liner manner, and much more. The presentation is masterful.

Chapter 5 covers quasi-Monte Carlo methods. The treatment is the best (read: most accessible) that I have read on this topic. Glasserman walks you through the construction of low-discrepancy numbers, starting with Van Der Corput sequences and proceeding to Halton, Faure, Sobol and other sequences. Algorithms are provided. Implementation and issues related to dimensionality are discussed.

The next three chapters return to financial engineering applications, covering the discretization of stochastic processes, estimation of factor sensitivities, and the pricing of American options. A lot of material is covered, and the treatment is excellent.

The book closes with a chapter on risk management applications. The topic deserves its own book (or books), so Glasserman becomes somewhat cryptic. There is plenty of information on variance reduction techniques for value-at-risk. You will find this more accessible if you first read my own (2003) treatment, but certainly follow up with Glasserman. He offers his own perspective and a different mix of techniques. Glasserman also offers a very brief discussion of credit risk modeling. If you are interested in variance reduction in this context, see the more in-depth treatment of Arvanitis and Gregory (2002).