Stochastic Implied Volatility: A Factor-Based Model (Lecture Notes in Economics and Mathematical Systems)

This book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows for the integrated and consistent pricing and hedging, risk management, and trading of equity index derivatives as well as volatility derivatives. In the first part, the book develops a unifying theory for the analysis of contingent claims under both the real-world measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of transaction data, the second part of the book provides extensive statistical analyses on the dynamics of the implied volatility surface of German DAX options and proposes a four-factor model to describe its evolution. The model is validated and tested on market data. The final part deals with potential applications of the model in the fields of exotic option pricing, value at risk, and volatility trading. This monograph is based on my Ph.D. thesis, which was accepted in Jan uary 2004 by the faculty of economics at the University of Augsburg. It is a great pleasure to thank my supervisor, Prof. Dr. Manfred Steiner, for his scientific guidance and support throughout my Ph.D. studies. I would also like to express my thanks to Prof. Dr. Gunter Bamberg for his comments and suggestions. To my colleagues at the department of Finance and Banking at the U ni versity of Augsburg, I express my thanks for their kind support and their helpful comments over the past years. In particular, I would like to thank Dr. Bernhard Brunner for many interesting discussions and also for the careful revision of this manuscript. At risklab germany GmbH, Munich, I would first of alllike to thank Dr. Gerhard Scheuenstuhl and Prof. Dr. Rudi Zagst for creating an ideal environ ment for research. I would also like to express my thanks to my coIleagues. It has been most enjoyable to work with them. In particular, I would like to thank Dr. Bernd Schmid. Our joint projects on stochastic implied volatil ity models greatly influenced this work. I am also indebted to Anja Fischer for valuable contributions during her internship and Didier Vermeiren (from Octanti Associates) for carefuIly reading the manuscript." Content: Front Matter....Pages I-XI Introduction....Pages 1-7 Continuous-time Financial Markets....Pages 9-22 Implied Volatility....Pages 23-57 The General Stochastic Implied Volatility Model....Pages 59-72 Properties of DAX Implied Volatilities....Pages 73-113 A Four-Factor Model for DAX Implied Volatilities....Pages 115-144 Model Applications....Pages 145-185 Summary and Conclusion....Pages 187-191 Back Matter....Pages 193-235 Reinhold Hafner. Thesis (doctoral) - Universität, Augsburg, 2004.