The rate of convergence of option prices on the asset following a geometric Ornstein–Uhlenbeck process

Abstract

The paper contains a discrete approximation scheme for the price of asset modeled by a geometric Ornstein–Uhlenbeck process. The idea is to consider Euler-type discrete-time approximations with the increments of the Wiener process replaced by i.i.d. bounded vanishing symmetric random variables. It is shown that the prelimit and limit markets are arbitrage-free, prelimit market is incomplete and admits the minimal martingale measure, and the limit market is complete. The rate of convergence of option prices is estimated using the classical results on the rate of convergence of the distributions of sums of nonidentically distributed random variables to the normal law.