Early in his career, Paul Wilmott was a university professor. He made a name for himself when he teamed up with Dewynne and Howison to publish a (1993) book on derivatives pricing that took the financial engineering world by storm. That book didn't present new theories so much as describe in practical but rigorous terms how the emerging theories of financial engineering should be used on a trading floor to price exotic derivatives. Although seriously out of date, that book remains a classic of finance.

Wilmott went on to leave academia and focused on media projects. He has a derivatives website and a magazine named after himself. He also published another book on financial engineering. That went through many editions and name changes. The current incarnation of that book is the topic of this review: Paul Wilmott on Quantitative Finance, 2nd Edition.

The book is a massive three-volume set focusing primarily on financial engineering but with discussions of topics such as portfolio theory, value-at-risk and duration. There is also a bizarre chapter in which Wilmott comments that technical analysis is probably so much "bunk" but then goes on to explain trend analysis, wave theory, candle sticking and head-and-shoulder patterns nonetheless!

The biggest criticism of the book is that it reflects outdated thinking. It largely presents the state-of-the-art in financial engineering as it existed in 1996, back when Wilmott was still a scholar. The book has been updated in some respects. For example, it discusses credit derivatives, CDOs and intensity models for credit risk. The meat of the book—its discussions of financial engineering for traditional underliers like equities or interest rates—is out of touch with current practices in 2006. Back in 1996, derivatives were priced by solving the Black-Scholes partial differential equation (PDE) using boundary conditions determined by the nature of the instrument being priced. Today, that is hardly ever done anymore. Instruments are routinely priced using risk neutral valuation as formalized by the Fundamental Theorem of Asset Pricing (FTAP). This book briefly mentions risk neutral valuation here and there. It doesn't mention the FTAP. Its in-depth discussions focus almost entirely on the valuation of derivatives using PDEs.

Mathematically, the book is not too advanced. Wilmott thinks and writes like an engineer. This has the advantage that he offers the sorts of practical insights you would expect from a seasoned hands-on engineer. I love his discussion of Jensen's inequality. His motivation of the market price of risk is also wonderful.

It has the disadvantage that mathematical derivations are more casual motivations than actual proofs. In one derivation, he starts off using simple financial returns. By the end, these have mysteriously changed to log financial returns. Reading Wilmott's derivations, I am reminded of the saying "good enough for government work"—but financial engineering isn't government work.

There is a tremendous amount of information here. I think anyone with an interest in financial engineering will benefit immensely from flipping through the book's three volumes. However, the book is not a good vehicle for first learning financial engineering. I have already mentioned it being outdated. Other shortcomings are a lack of exercises and discussions that are too cursory for a beginner—or even intermediate—financial engineering student to actually base implementations on.

It is hard to recommend this book. Then again, it is hard to not recommend it. The book has many shortcomings, but it has much of value. It is kind of unique. [July 1, 2006]