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

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.

Jean-Pierre Fouque studied at the University Pierre et Marie Curie in Paris. He held positions at the French CNRS and Ecole Polytechnique, and at North Carolina State University. Since 2006, he is Professor and Director of the Center for Research in Financial Mathematics and Statistics at the University of California, Santa Barbara. George Papanicolaou was Professor of Mathematics at the Courant Institute before coming to Stanford University in 1993. He is now Robert Grimmett Professor in the Department of Mathematics at Stanford Ronnie Sircar is a Professor in the Operations Research and Financial Engineering department at Princeton University, and an affiliate member of the Bendheim Center for Finance and the Program in Applied and Computational Mathematics. Knut Slna is a Professor in the Department of Mathematics at the University of California at Irvine. He received his undergraduate and Master's degrees from the Norwegian University of Science and Technology, and his doctorate from Stanford University. He was an instructor at the Department of Mathematics, University of Utah before coming to Irvine.