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

TL;DR

This paper develops a semi closed-form approximation formula for pricing up-and-out barrier options under stochastic volatility models, including SABR, using an asymptotic expansion method and validates it numerically.

Contribution

It introduces a novel asymptotic expansion approach for barrier option pricing under complex stochastic volatility models.

Findings

The approximation formula closely matches numerical benchmarks.

The method is applicable to SABR and similar models.

Numerical examples confirm the accuracy of the approximation.

Abstract

This paper derives a new semi closed-form approximation formula for pricing an up-and-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 (2012). We also demonstrate the validity of our approximation method through numerical examples.