Modelling the Chinese crude oil futures returns through a skew-geometric Brownian motion correlated with the market volatility index process for pricing financial options

Abstract

In this paper we model the dynamics of the Chinese crude oil futures returns by using a skew-geometric Brownian motion correlated with the market volatility, which is taken as a square-root stochastic process. We use the OVX index data as proxy for market volatility. We validate the proposed model in terms of accuracy of its calibrations through an in-sample simulation. Instead, out-of-sample simulations are used to show that a correlated skew-geometric Brownian motion is more appropriate for modelling the Chinese returns compared to a single skew-geometric Brownian motion in terms of forecasts. Furthermore, we price an American call option on the Chinese futures by using a recursively scheme based on a closed-form formula, and an alternative Monte Carlo approach, for the related European call option. We show that our call price estimates are very close to market values and our model generally outperforms many benchmarks in literature, such as the Barone-Adesi and Whaley formula and its generalizations.