Convergence Rate of the High-Order Finite Difference Method for Option Pricing in a Markov Regime-Switching Jump-Diffusion Model

Abstract

The high-order finite difference method for option pricing is one of the most popular numerical algorithms. Therefore, it is of great significance to study its convergence rate. Based on the relationship between this algorithm and the trinomial tree method, as well as the definition of local remainder estimation, a strict mathematical proof is derived for the convergence rate of the high-order finite difference method for option pricing in a Markov regime-switching jump-diffusion model. The theoretical result shows that the convergence rate of this algorithm is O(Δτ) . Moreover, the results also hold in the case of Brownian motion and jump-diffusion models that are specialized forms of the given model.