Financial Derivatvies in Theory and Practice, Revised Edition [Hardcover]

The book is divided into two parts: Theory (212 pages) and Practice (159 pages). The first part surveys the mathematics of no-arbitrage pricing theory. It starts by a succinct and rigorous account on stochastic calculus (including basic properties on Wiener process, theory of martingales, and a complete development of stochastic integration w.r.t. continuous semimartingales), written in the spirit of the monograph by Revuz and Yor. The section on SDEs is particularly detailed and covers many topics (e.g. strong and weak solutions, description of the Yamada-Watanabe construction) that are not typically found in texts on finance. All technicalities are treated with due care, and some parts of the text are accompanied with exercises. The first part concludes with two sections on pricing by no-arbitrage and term structure models. Overall this part of the book is masterfully written and it is certain to please a mathematically-inclined reader (I'm not sure about the others).

The second part deals with application of the theory in pricing, with emphasis on interest-rate derivatives. After starting off with an interesting discussion about the real-world modelling issues (risk-free vs. "real-world" probability measure, calibration and dimension reduction), the authors introduce basic fixed income instruments (FRAs, caps, floors, swaps, etc) and proceed by developing no-arbitrage pricing using the standard Black's formula. The next four sections containing material on pricing exotic European derivatives largely follow authors' previously published papers. The book concludes with several sections on pricing exotics and path-dependent derivatives that start with a nice accounts on short-rate (Vasicek-Hull-White) model and market models. The treatment of the latter also gives a systematic development of the drift correction factors for various choices of numeraires. The last section on Markov functional modelling follows one of the authors' papers. One detail that is obviously missing from this part is the treatment of hedging of interest-rate derivatives. Also additional comparisons between existing and the Markov functional model seem to be in order.

The book is divided into two parts, Theory and Pratice.
The theory part is a course on stochastic processes and stochastic integration: martingales, local martingales, semimartingales, Ito integrals and Ito formulas are developed with a high level of mathematical rigor. This part is definitely not accessible to a non mathematician. On the other hand it does not contain anything new and most proofs are not given...

The second part is about applications to finance, but it is focused on interest rate models, which seems to be the expertise of the authors. LIBOR and swap market models and interest rate derivatives are explained in detail but only at a theoretical level; the subtitles on "calibration" do not contain any useful material not is there a single numerical or empirical example of market data/ model calibration. Monte Carlo simulation, finite difference methods and tree methods are not even discussed...

The relation between the two parts is not clear: it seems that one author wrote the first part while the author wrote the second part...for example, the first part takes great care to distinguish predictable and optional processes and to define integrals of predictable processes while the second part only uses continuous models for which this distinction is useless.
Also, the first part develops the Kunita Watanabe decomposition and studies sets of martingale measure and their extremal elements, a prelude to the study of incomplete markets.
These tools are not put to use in the second part.

It could be a good reading for graduate students in probability curious to know about mathematical finance but not to professionals in this field.