This book addresses problems
in financial mathematics of pricing and hedging derivative securities in an environment of
uncertain and changing market volatility. These problems are important to investors from
large trading institutions to pension funds. It presents mathematical and statistical
tools that exploit the bursty nature of market volatility. The mathematics is introduced
through examples and illustrated with simulations and the modeling approach that is
described is validated and tested on market data. The material is suitable for a one
semester course for graduate students who have had exposure to methods of stochastic
modeling and arbitrage pricing theory in finance. It is easily accessible to derivatives
practitioners in the financial engineering industry.
... provides a good overview
to the theoretical and practical problems when dealing with stochastic volatility.
Ralf Korn, Mathematical Methods of Operations Research
... something genuinely new
... explained with admirable clarity in this extremely well-written book ... (which) is
short and to the point, and the production quality is high. Buy it.
Mark Davis, Risk Magazine
... 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.
P. A. L. Embrechts, Publication of the International Statistical Institute
Thanks to a well-written
first chapter on the Black-Scholes theory of derivative pricing, the book is essentially
self-contained if one has some basic knowledge in stochastic methods and arbitrage
pricing. Its style is largely informal which makes it also accessible to practitioners in
the finance industry.
M. Schweizer, Zentralblatt für Mathematik
... an excellent book that
succeeds admirably in all its aims. It can satisfy both practitioners and researchers at
the same time. It is very well written and it is concise and informative.
Angelos Dassios,The Statistician
Contents
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. Symptotics 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
rates models
201 pages