Convergence Rate Analysis for the Continuous-Time Markov Chain Approximation of Occupation Time Derivatives and Asian Option Greeks

Abstract

This paper establishes the second-order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing continuously monitored occupation time derivatives (step options, conditional Asian options) and arithmetic Asian options and their Greeks. We fill the gap in the current literature on the analysis of CTMC approximation errors for pricing Asian options by not only rigorously proving the exact second order convergence rate but also developing corresponding error and convergence analysis for the Greeks through the novel use of pathwise method and Malliavin calculus techniques. We further extend the scope of the analysis of the CTMC approximation method to the case of general occupation time derivatives (e.g. step options) and the recently introduced conditional Asian options, and then propose a novel CTMC scheme for their valuation. We carry out a detailed error and convergence analysis of the algorithms and numerical experiments substantiate the theoretical findings.

Keywords: Continuous-Time Markov Chains, Error Analysis, Non-Uniform Grids, Convergence Rates, Path-Dependent Options, Greeks, Matrix-Analytic Method, Laplace Inversion

JEL Classification: G63, G13