Modeling Energy Spreads with a Novel Mean-reverting Stochastic Process

Mir Hashem Moosavi1

University of Western Ontario (UWO)

Abstract

The spread between two related energy prices is a very important quantity throughout energy finance. Of particular interest are the spreads between different energy types, location spreads, and calendar spreads. At times it is appropriate to consider the spread as a distinct process from the underlying price processes which may also be modeled directly.  We introduce a new mean-reverting random walk, derive its continuous stochastic differential equation and obtain some analytical results about its solution.  This new mean-reverting process is compared with the Vasicek process and its advantages discussed. We showed that this new model for spread dynamics is capable of capturing the possible skewness, kurtosis, and  heavy tails in the transition density of the price spread process. Since the analytical transition density is unknown for this nonlinear stochastic process, the local linearization method is deployed to estimate the model parameters.  We apply this method to empirical data for modeling the spread between West Texas Intermediate (WTI) crude oil and West Texas Sour (WTS) crude oil.

Keywords: Commodity spread process; Cointegration; Mean-reversion; Energy markets; Mean-reverting random walk