Title DERIVATIVES IN FINANCIAL MARKETS WITH STOCHASTIC VOLATILITY.
Author J.P. Fouque, G. Papanicolaou and K.R. Sircar.
Publisher Cambridge University Press, 2000, pp. xiv + 201, £30.00/US$49.95.

Contents:
Introduction
1. The Black-Scholes theory of derivative pricing
2. Introduction to stochastic volatility models
3. Scales in mean-reverting stochastic volatility
4. Tools for estimating the rate of mean reversion
5. Asymptotics for pricing European derivatives
6. Implementation and stability
7. Hedging strategies
8. Application to exotic derivatives
9. Application to American derivatives
10. Generalizations
11. Applications to interest-rate models

Readership: Graduate students in quantitative finance, financial engineers

From the start, financial engineers knew that the conditions on
constant volatility in the basic Black-Scholes-Merton (BSM) approach
to option pricing and hedging was only an approximative one. Early on,
smile effects pointed at a need to model beyond this constant
volatility. As a consequence, the world of GARCH modelling together
with stochastic volatility models emerged. The present book discusses
the latter. Its first half contains a very readable introduction to
the probabilistic theory of stochastic volatility
modelling. Gradually, the authors pencil in the statistical proofs of
volatility bursts and fast mean reversion. Based on these empirical
facts, an asymptotic expansion approach is used to correct the pricing
and hedging formulae in the classical BSM world. Along the way, two
new "Greeks", epsilon and kappa, are introduced. They correspond to
the third and fourth derivative of the classical Black-Scholes price
with respect to the price of the underlying. The corrected formulae
are tested on some real examples including more exotic options. The
book is well written and makes ideal reading for a graduate course on
mathematical finance. The authors took great care in making their
ideas clear. I support this text strongly and recommend it for the
intended audience.  Reviewer: Institute ETH-Zürich Place Zürich,
Switzerland Name P.A.L. Embrechts