An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model (Forthcoming in JSIAM Letters”)”

Abstract

This paper derives a new semi closed-form approximation formula for pricing an upand-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada [1]. We also demonstrate the validity of our approximation method through numerical examples.