A Note on Pricing Barrier Options Under a Stochastic Volatility Model: An Asymptotic Expansion with Static Hedging

Abstract:     
This short note proposes an approximation method of pricing barrier options under stochastic volatility environment by applying an asymptotic expansion approach combined with a static hedging method. In particular, through numerical examples it shows that the fifth-order normal approximation of an asymptotic expansion scheme (Shiraya-Takahashi-Toda, Takahashi-Takehara-Toda) with a modification of a static hedging method by Fink provides good approximations under the lambda-SABR model.

Keywords: barrier option, knock-out option, static hedge, asymptotic expansion, stochastic volatility, lambda-SABR model

Working Paper Series