The Convergence Speed of Pricing European-Style Derivatives under Lattice Models

Abstract

It is known that the Black-Scholes model can be well approximated by lattice models such as the Cox-Ross-Rubinstein (CRR) model in Cox, Ross, and Rubinstein (1979). The orders of convergence of several lattice models have been shown in Leisen and Reimer (1996). In this study, we consider a derivative pricing problem where the value of the underlying asset follows a more general stochastic process instead of a geometric Brownian motion (GBM). In addition, we do not focus on only European call options. Instead, a more general European-style derivative is allowed. We provide a different proof from the one in Leisen and Reimer (1996) and show that the order of convergence of lattice approximation used to price European-style derivatives is 1.