THE RATE OF CONVERGENCE OF OPTIONS PRICES WHEN SAMPLING THE ORNSTEIN-UHLENBE GEOMETRIC PROCESS BY BERNOULLI PRICE HOPPING JUMPS

The paper contains the discrete approximation scheme for the price of asset that is modeled by geometric Ornstein-Uhlenbeck process. The idea is to consider Euler-type discrete-time approximations but to replace the increments of the Wiener process with Bernoulli` s independent identically distributed random variables. The rate of convergence of both objective and fair option prices is estimated using the classical results of the rate of convergence to the normal law of the distribution function of the sum of non-identically distributed random variables. The transition from the objective to the martingale measure and what happens with option prices in the model under such transformation, is analyzed.