Jump-diffusion Model for Crude Oil Spot Price Process: Parameter Estimation for Predicting the Market

Abstract

The jump-diffusion model incorporates a jump component to a diffusion process. It has been very popular in modelling asset prices, foreign exchange and other securities whose dynamics are non-Gaussian. Crude oil spot price is also modelled as a jump-diffusion process. Several methods such as characteristic function CF, maximum likelihood estimation (MLE), method of cummulants, etc. have been used for parameter estimation of the jump-diffusion model. These approaches are inefficient, and estimating parameters of the jump-diffusion model has been challenging. The inability to effectively estimate parameters of the jump-diffusion model makes market prediction and price forecasting challenging. Generation of viable mathematical tool for expressing market perceptions is difficult. The challenges were surmounted, by using the Yuima package in R, for estimating, parameters of the jump-diffusion model. Data for four crude types in the Niger-Delta over the period January 2005 - December 2009 was used. The Yuima package yields accurate estimates, which can help to interpret market behaviour, and possibly make price forecasting and market prediction less challenging.