9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract

A Market Model for Stochastic Implied Volatility

Philipp J. Schönbucher

Department of Statistics, Faculty of Economics, Bonn University

In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied Black-Scholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. The conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and its numerical implementation is discussed.