Commodities Prices Modeling Using Gaussian Poisson-Exponential Stochastic Processes, a Practical Implementation in the Case of Copper. Presented at ECMS 2009

Abstract

Due to an assignment, received from a Chilean mining company, to value a copper mine with an estimated life span of several decades, we implemented a model of copper prices using mean reversion with Gaussian Poisson exponential jumps.

The parameters of the model are extracted from the copper prices series. The exponential distributions of the jumps are estimated via a standard simulation program using best likelihood methods.

Until the model was implemented, the company had been using a long term mean price to estimate mining projects’ cash flows. This approach had worked satisfactorily given that, as shown in the Chart 1, the average price of copper had ranged around 100 cents of USD per pound between 1996 and 2004.

However, a turnaround in the cycle occurred in 2004, with prices going up between that year and 2008 to reach a mean value of 325 ç/pound. At the end of 2008 the price dropped down up to the level of 150 ç/pound. The prices series analysis suggests the existence of mean reversion with stochastic jumps especially from 2006.

Keywords: Commodities prices modelling, Gaussian Poisson, Exponential Processes