Analysis of Markov Chain Approximation for Option Pricing and Hedging: Grid Design and Convergence Behavior

Continuous time Markov chain approximation is an intuitive and powerful method for pricing options in general Markovian models. This paper analyzes how grid design affects the convergence behavior of barrier and European... [ view full abstract ]

Continuous time Markov chain approximation is an intuitive and powerful method for pricing options in general Markovian models. This paper analyzes how grid design affects the convergence behavior of barrier and European options in general diffusion models. Using the spectral method, we obtain sharp estimates for the convergence rate of option price, delta and gamma for non-uniform grids.  Our analysis inspires us to propose a novel class of non-uniform grids, which ensures that convergence is not only second order, but also smooth, which makes extrapolation applicable to achieve even higher convergence rate. The extrapolation also works in jump models.