This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR...

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 paper proposes a new deep learning-based algorithm for high-dimensional Bermudan option pricing. This is the first study for arbitrary order discretization scheme in the Bermudan option pricing or the dynamic programming problems. The price of Bermudan option is well approximated by...