Weak Approximation for a Black-Scholes Type Regime Switching Model

We provide a Monte Carlo simulation method for a European type option under a regime switching type Black-Scholes model where the volatility is a discontinuous step function which takes n+1 different values depending on the value of the underlying within n+1 disjoint partition intervals. Our simulation method is based on a combination of the Euler scheme which is used in the case that the process is away from the boundary points of the partition intervals and the skew Brownian motion in the case that it the process in near the boundary points of the partition intervals. We show that the weak error of approximation is exponentially small for the proposed method and show some simulation results.