Empirical Martingale Simulation for Asset Prices

Abstract

This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies the rational option pricing bounds. The EMS yields a substantial error reduction for the price estimate and can be easily coupled with the standard variance reduction methods. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money or longer-maturity options. The option price estimate based on the EMS is found to exhibit a minor small-sample bias only in few occasions. An analysis of the trade-off between computing time and price accuracy reveals that the EMS dominates the conventional simulation methods.

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