Theory of Probability and Mathematical Statistics
Rate of convergence of option prices by using the method of pseudomoments
Yu. S. Mishura, E. Yu. Munchak
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Abstract: A sequence of discrete time financial markets is considered in the scheme of series. The rate of convergence for put and call option prices in the discrete-time model is studied if the prices of risky assets weakly converge to those in the Black-Scholes model. This rate of convergence is of order O(n^{-1}), where n is the number of trading periods on a fixed time interval for the prelimit model. The result follows from an author theorem concerning the rate of convergence in the central limit theorem for identically distributed random variables, and the latter is obtained by using the method of pseudomoments.
Keywords: Financial markets in discrete and continuous time, scheme of series, pseudomoments, rate of convergence, option prices, Black-Scholes model
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