ON DERIVATIVES OF CLAIMS IN COMMODITY AND ENERGY MARKETS USING A MALLIAVIN APPROACH

Abstract

In this paper we investigate the recently introduced Malliavin approach compared to more classical approaches to find sensitivities of options in commodity and energy markets. The Malliavin approach has been developed in two papers by Lions et. al (Lions 1999 and Lions 2001). In commodity and energy markets, some special dynamics for the underlying security and some new products different from Black \& Scholes markets are encountered. In addition to investigating the numerical values of the expressions by conventional Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods, we apply an adaptive approach developed in two recent papers by Dahl (Dahl 2001 and Dahl 2002). This adaptive method is also applied to the so called Localized Malliavin approach developed in the paper Lions 2001. The numerical results show that we can get substantial variance reduction by choosing sophisticated methods for the simulations, and that the Malliavin approach is a very powerful tool for formulating the sensitivity estimators.