Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives

Fouque, Jean-Pierre; Papanicolaou, George; Sircar, Ronnie; Sølna, Knut

Hardcover

ISBN 10: 0521843588 ISBN 13: 9780521843584

Publisher: Cambridge University Press, 2011

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Book Description:

This research monograph in financial mathematics can also be used as a graduate-level textbook. It explains financial models in which volatility of assets changes randomly over time. These are analyzed with a powerful approximation method and tested on financial data. More advanced topics are discussed in later chapters.

Synopsis:

This book builds on previous and current research by the four authors, including results introduced in the book Derivatives in Financial Markets with Stochastic Volatility. Recent research demonstrates that the introduction of two time scales in volatility, a fast and a slow, is needed and efficient for capturing the main features of the observed term structure of implied volatility. For practitioners, the modeling of the implied volatility consistent with no-arbitrage is crucial. The authors present an approach to this problem which consists in combining singular and regular perturbation techniques. The book will serve a dual purpose: present 'off the shelf' formulas and calibration tools for practitioners, and introduce, explain and develop the mathematical framework to handle the multi-scale asymptotics. Detailed presentation of the analysis as well as a thorough insight into the modeling approach makes this an excellent text for a second level graduate course in financial and applied mathematics.