Stochastic Implied Volatility: A Factor-Based Model

✍ Scribed by Dr. Reinhold Hafner (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 2004
• Tongue: English
• Leaves: 234
• Series: Lecture Notes in Economics and Mathematical Systems 545
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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