Customer Reviews

Engineering BGM (Chapman & Hall/CRC Financial Mathematics Series)

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Upon finding the term "engineering" in the title of a book, our reader might fairly expect a clearly written, practical, and non-theoretical exposition from the author. This is not the case with this text (much to the disappointment of this reviewer). The author has prepared an extremely terse research style monograph. The book, which runs just over 200 pages, is divided into 17 chapters and a multi-section appendix. None of the chapters provides an excess of detail.

One of the interesting features of the author's brief exposition is the "slickness" of the derivations of some of the central formulas. For example, in Chapter 1, the author provides a half-page derivation of the celebrated HJM drift condition. The proof is correct, but is given without reference to the main tools used, such as the stochastic Leibniz rule for differentiating under the Ito integral, and the stochastic Fubini theorem. Our reader is left to infer the use of these techniques and chase down the references on her own.

Another curious feature, also found in Chapter 1, is the non-standard definition of the T-forward measure, a crucial element of the now classical BGM model. The author never proves that his new definition is equivalent to the usual change-of-numeraire approach found in, say, Brigio & Mercurio's Interest Rate Models - Theory and Practice. This requires an independent derivation on the part of the reader in order to keep the remainder of the exposition from being "muddy".

The material on calibration techniques in Chapter 7 is a bit more engineering-minded with several psuedo-algorithms presented in step-by-step fashion. However, no cautions & warnings are given with regards to numerical implementation of these steps. A discussion of the rate of convergence and/or failure of convergence is strangely omitted. The material on simulation in Chapter 9 starts out describe Glasserman-type simulation. The reader will probably be better served skipping the author's 5 page treatment and instead studying Glasserman's Monte Carlo Methods in Financial Engineering

Overall, the author's 17 chapters provide a broad outline of the material that a modern interest modeler should master to develop state-of-the art valuation models for exotic interest rate derivatives and mortgage-backed securities. Unfortunately, the author's exposition is neither sufficiently detailed, nor practical enough to allow for the engineering of such models solely from reading this text.

The financial instruments described by the book are quite powerful. So too is the level of maths needed to model them. The book is for a analyst or programmer, who is already well versed in financial simulations.

To be sure, there may be a diminution in the need for such instruments, in the near term. As the ongoing and massive losses in financial markets has been attributed in no small part to the (reckless?) use of some instruments like CDOs. But looking at the longer term, the ideas in the book are unlikely to entirely fade. There will still be a need for some practioners who understand its methods.

This is probably one of the best BGM books in the market. HJM and BGM models are studied in parallel. Shifted Lognormal distribution to model vol skew is very well explained.