A Test of the Use of the Implied Volatility Function Model to Price Exotic Options

Abstract

Researchers such as Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) have proposed a one-factor model for asset prices that is exactly consistent with all European option prices. In this model, which we refer to as the implied volatility function (IVF) model, the asset price volatility is a function of both time and the asset price. Practitioners often use the IVF model to price exotic options. This paper explores the validity of this. It does so by assuming a two-factor stochastic volatility model for the asset price and examining the way the IVF model prices compound options and barrier options. We find the model works well for compound options, but sometimes gives rise to large pricing errors for barrier options.