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

Erscheinungsjahr 2011
ISBN: 978-0-521-84358-4
Verlag: Cambridge University Press

Buch, Englisch, 456 Seiten, Format (B × H): 182 mm x 256 mm, Gewicht: 983 g

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.

Autoren/Hrsg.

Fouque, Jean-Pierre

Papanicolaou, George

Sircar, Ronnie

Sølna, Knut

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines

Inhaltsverzeichnis

Introduction; 1. The Black–Scholes theory of derivative pricing; 2. Introduction to stochastic volatility models; 3. Volatility time scales; 4. First order perturbation theory; 5. Implied volatility formulas and calibration; 6. Application to exotic derivatives; 7. Application to American derivatives; 8. Hedging strategies; 9. Extensions; 10. Around the Heston model; 11. Other applications; 12. Interest rate models; 13. Credit risk I: structural models with stochastic volatility; 14. Credit risk II: multiscale intensity-based models; 15. Epilogue; Bibliography; Index.

Über Autor(innen)

Fouque, Jean-Pierre
Jean-Pierre Fouque studied at the University Pierre and Marie Curie in Paris. He held positions at the French CNRS and École Polytechnique, and at North Carolina State University. Since 2006, he has been Professor and Director of the Center for Research in Financial Mathematics and Statistics at the University of California, Santa Barbara.

Sølna, Knut
Knut Sølna is a Professor in the Department of Mathematics at the University of California, 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 moving to Irvine.

Sircar, Ronnie
Ronnie Sircar taught for three years at the University of Michigan in the Department of Mathematics before moving to Princeton University in 2000. He is now a Professor in the Operations Research and Financial Engineering Department at Princeton and an affiliate member of the Bendheim Center for Finance and the Program in Applied and Computational Mathematics.

Papanicolaou, George
George Papanicolaou was Professor of Mathematics at the Courant Institute before moving to Stanford University in 1993. He is now Robert Grimmett Professor in the Department of Mathematics at Stanford.

Jean-Pierre Fouque studied at the University Pierre and Marie Curie in Paris. He held positions at the French CNRS and École Polytechnique, and at North Carolina State University. Since 2006, he has been 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 moving to Stanford University in 1993. He is now Robert Grimmett Professor in the Department of Mathematics at Stanford.

Ronnie Sircar taught for three years at the University of Michigan in the Department of Mathematics before moving to Princeton University in 2000. He is now a Professor in the Operations Research and Financial Engineering Department at Princeton and an affiliate member of the Bendheim Center for Finance and the Program in Applied and Computational Mathematics.

Knut Sølna is a Professor in the Department of Mathematics at the University of California, 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 moving to Irvine.