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[4],Takahashi-Takehara-Toda[7]) with a modification of a static hedging method by Fink[1] provides good approximations under the λ-SABR model.
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