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A Market Model for Stochastic Implied Volatility

By Philpp J. Schönbucher

Abstract

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.option pricing, stochastic volatility, implied volatility

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