Derivatives in financial markets with stochastic volatility

This book addresses problems in the 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. The book 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 modelling approach that is described is validated and tested on market data. The material is easily accessible to derivatives practitioners in the financial engineering industry.

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
• Applications to American derivatives
• Generalisations
• Applications to interest rates models.