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Empirical Martingale Simulation for Asset Prices

Jin-Chuan Duan and Jean-Guy Simonato ()

CIRANO Working Papers from CIRANO

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 rational option pricing bounds. The EMS also yields a substantial error reduction for the price estimate. The EMS can be easily coupled with the standard variance reduction methods to obtain greater computational efficiency. 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 options. Cette étude propose une modification simple aux procédures traditionnelles de calcul de prix des produits dérivés par simulation de Monte Carlo. La modification impose la propriété de martingale aux trajectoires simulées de la variable d'état sous-jacente. L'utilisation de cette procédure assure que l'estimé de prix respecte les bornes rationnelles d'option tout en diminuant de façon substantielle la variance des estimés de prix. La procédure peut aisément être jumelée aux méthodes traditionnelles de réduction de variance afin d'obtenir une plus grande efficacité. Une étude de simulation est présentée pour des options d'achat Européennes et Asiatiques. Les résultats indiquent que la méthode obtient des réductions substantielle de la variance des estimés de prix et ce, particulièrement pour les options in et at the money.

Keywords: Martingale; Option Pricing; Monte Carlo Simulation; GARCH; Asian Options; Martingale; Evaluation des Options; Simulation de Monte Carlo; GARCH; Options Asiatiques (search for similar items in EconPapers)
Date: 1995-10-01
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