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This paper derives a new semi closed-form approximation formula for pricingan up-and-out barrier option under a certain type of stochastic volatilitymodel including SABR model by applying a rigorous asymptotic expansion methoddeveloped by Kato, Takahashi and Yamada (2012). We also demonstrate thevalidity of our approximation method through numerical examples.

An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model