The Black-Scholes model for pricing FX and equity options has become ubiquitous. However, it is always used with a pinch of salt. In particular, traders typically use different volatilities when pricing options with different strikes, a practice which makes no sense in the context of the model, but is a very effective way of compensating for its deficiencies. This is known as the smile effect from the shape of the volatility graph.
Rebonato's new book sets out to examine these deficiencies and presents various alternative models. For each model, he examines the validity of its assumptions and predictions, convincingly demonstrating that fear of jumps is a major cause of smiles.
The other major theme of the book is that volatility and correlation are quite different objects for interest rate derivatives than for FX and equity options. In the context of BGM models, he shows that the shape of the volatility function of forward rates is the major cause of decorrelation, rather than actual instantaneously uncorrelated movements.
This book is not a first book on mathematical finance but it is accessible and is a must read for anyone involved in the pricing of derivative products.