Advances in pricing commodity futures: Multifactor models
The purpose of this paper is to obtain the risk-neutral drift of the state variables directly from market data in a multifactor commodity futures model. Note that the risk-neutral drift is a key factor in the general asset pricing theory but it is not observable. In this paper, we derive some exact results which relate the risk-neutral drifts to the slope of the commodity futures price jointly with the factors. This fact allows us to estimate some of the coefficients of the pricing partial differential equation directly from the futures data available in the markets. Moreover, we do not have to estimate either the physical drift or the market price of risk. Therefore we considerably reduce the number of functions to estimate and, as a consequence, we reduce the computational cost as well as the misspecification error. In order to investigate the finite sample properties of this approach we carry out some numerical experiments. Finally, an application to crude oil and natural gas futures contracts traded at the New York Mercantile Exchange (NYMEX) is also illustrated. (C) 2011 Elsevier Ltd. All rights reserved.
commodity futures no-arbitrage stochastic process numerical methods martingale