A drift‐free simulation method for pricing commodity derivatives

Abstract

Having in view the pricing of commodity derivatives in Libor Market Model (LMM) setting, we first analyze the set of basic rates we need to formulate the model by using the spanning tree concept taken from graph theory. Next, we present an efficient procedure for Monte Carlo simulation of the dynamics of the rates associated to LMM, avoiding the presence of the rates dependent drifts (drift‐free simulation) and the presence of negative deflated bond prices and negative forward rates. The method is based upon a new parameterization of the martingales introduced by Glasserman and Zhao and it is extended to a Cross‐Market Model for commodities. Finally, a particular example of commodity derivative (spread option) pricing problem is considered. Copyright © 2014 John Wiley & Sons, Ltd.