A Semi-group Expansion for Pricing Barrier Options

TL;DR

This paper introduces a semi-group expansion technique for efficiently approximating the prices of barrier options under stochastic volatility models, validated through numerical experiments.

Contribution

It develops a novel semi-group expansion scheme for second-order PDEs in barrier option pricing, providing a practical approximation formula.

Findings

The method accurately approximates barrier option prices.

Numerical experiments confirm the validity of the approximation.

The approach improves computational efficiency for complex models.

Abstract

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.