The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

Abstract

In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we obtain the futures risk premia in both cases and we observe that for long maturities the term structure of the risk premia is negative. Moreover, the Exponential distribution provides the highest premia in absolute value.

Residual Shape Risk on Natural Gas Market with Mixed Jump Diffusion

“…The evaluation of RSR requires modelling of prices of evaluated commodity, in our application natural gas. The literature (Baum et al 2018;Benth et al 2008;Borovkova & Mahakena 2015;Brix et al 2018;Cao et al 2018;Gomez-Valle et al 2017a;Hsu et al 2017;Mason & Wilmot 2014;Mishra & Smyth 2016;Safarov & Atkinson 2017) shows that the gas prices and energy commodities in general have quite complex price distribution as compared to financial assets. Gas prices commonly depart from normality by exhibiting heavy tails and a leptokurtic shape (Benth et al 2008).…”