Derivatives in Financial Markets with Stochastic Volatility

This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.

Jean-Pierre Fouque (Author), George Papanicolaou (Author), K. Ronnie Sircar (Author)

9780521791632, Cambridge University Press

Hardback, published 3 July 2000

218 pages
23.8 x 16.1 x 1.8 cm, 0.44 kg

'I consider this book to be an outstanding achievement. the theory is practically very relevant and scientifically on a high level. The book also serves as a good introduction into the basic ideas of Mathematical Finance, putting emphasis on the techniques of partial differential equations. It can therefore also be recommended to readers with little knowledge about Mathematical Finance.' Monatshefte für Mathematik

This book, first published in 2000, 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.

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.

Subject Areas: Stochastics [PBWL], Applied mathematics [PBW], Finance [KFF]