Theory of Probability and Mathematical Statistics
Rate of convergence of option prices for approximations of the geometric Ornstein-Uhlenbeck process by Bernoulli jumps of prices on assets
Yu. S. Mishura, Ye. Yu. Munchak
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Abstract: We consider the discrete approximation scheme for the price of an asset that is modeled by the geometric Ornstein-Uhlenbeck process. The approximation scheme corresponds to Euler type discrete-time approximations where the increments of the Wiener process are changed by independent identically distributed Bernoulli random variables. The rate of convergence of both objective and fair option prices is estimated by using the classical results on the rate of convergence to the normal law of the distribution functions of sums of identically distributed random variables. We analyze option prices and specific changes in a model where the martingale measure is used instead of the objective measure.
Keywords: Financial market, rate of convergence, Ornstein-Uhlenbeck process, option prices
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