Lévy Processes in Gold Option Modeling

Abstract

To price and hedge derivative securities, it is crucial to have a good model of the probability distribution of the underlying product. In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts. To overcome this drawback, the Lévy process was introduced to financial modeling. Today Gold futures markets are highly volatile. The purpose of this paper is to develop a mathematical framework in which American options on Gold futures contracts are priced more effectively. In this work, the Generalized Hyperbolic process, Normal Inverse Gaussian Process, Generalized Inverse Gaussian Process and Variance Gamma Process were used to model the future price. Then, option prices under the risk-neutral pricing process were calibrated and then authors attempt to infer the density forecast of future Gold prices at a given time horizon. Finally, Normal Inverse Gaussian was selected as the best model for Gold options by significant quantitative comparison between parsimonious models.