Crack spread option pricing with copulas

摘要

A copula-based approach for pricing crack spread options is described. Crack spread options are currently priced assuming joint normal distributions of returns and linear dependence. Statistical evidence indicates that these assumptions are at odds with the empirical data. Furthermore, the unique features of energy commodities, such as mean reversion and seasonality, are ignored in standard models. We develop two copula-based crack spread option models using a simulation approach that address these gaps. Our results indicate that the Gumbel copula and standard models (binomial, and Kirk and Aron (1995)) mis-price a crack spread option and that the Clayton model is more appropriate. We contribute to the energy derivatives literature by illustrating the application of copula models to the pricing of a heating oil–crude oil “crack” spread option.