Short description
This book addresses pricing and hedging derivative securities in uncertain and changing market volatility.
Long description
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.
Review
"Fouque, Papanicolau and Sircar have come up with something genuinely new in this area, explained with admirable clarity in this extremely well-written book...the book is short and to the point, and the production quality is high. Buy it." Risk Magazine "Though the topic discussed in the book is conceptually rather difficult, the book itself is highly readable. Since the book starts from scratch and the style is user friendly, it is in my opinion accessible to graduate students specializing in the field of financial mathematics and probability theory." Mathematical Reviews
Table of contents
- The Black
- Scholes theory of derivative pricing
- Introduction to stochastic volatility models
- Scales in mean
- reverting stochastic volatility
- Tools for estimating the rate of mean
- reversion
- Symptotics for pricing European derivatives
- Implementation and stability
- Hedging strategies
- Application to exotic derivatives
- Application to American derivatives
- Generalizations
- Applications to interest rates models