Strong consistency of the empirical martingale simulation option price estimator
In arbitrage-free economies the price of a derivative contract can be expressed as a discounted expectation of its payoff. If the expectation does not have a closed-form solution, one might use Monte Carlo simulation to estimate this expectation. Sometimes, however, even a large number of simulated paths does not lead to convergence since the degree of accuracy is inversely proportional to the square root of the number of simulated sample paths. Recently, \textit{J.-C. Duan} and \textit{J.-G. Simonato} [Manage. Sci. 44, No. 9, 1218--1233 (1998; Zbl 0989.91533)] proposed a method named empirical martingale simulation (EMS) by empirically imposing the martingale property on the simulated sample paths of the underlying asset price to avoid violation of the rational option pricing bounds. EMS has been employed for \textit{J.-C. Duan} and \textit{J. Z. Wei} [Pricing foreign currency and cross-currency options under GARCH, Working paper (2006)] due to its substantial reduction of simulation errors. Duan and Simonato (loc. cit.) proved that the EMS option price estimator is strongly consistent for Lipschitz-continuous payoffs as, e.g., in the Black-Scholes pricing framework. The authors of the present paper show the strong consistency of the EMS option price estimator for a class of payoffs (including e.g. self-quanto calls) larger than those studied by Duan and Simonato (loc. cit.). The authors also perform an assessment of the computational efficiency of the EMS.
scientific article; zbMATH DE number 5632906