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Analytic approximation formulae for European crack spread options

In this paper, we investigate and compare the pricing of European crack spread call options under different underlying models. New proposed univariate and explicit constant elasticity of variance (CEV) models are assumed and new analytic approximation formulae in the form of asymptotic expansions are derived. As well we derive an analytic approximation formula based on an explicit version of two correlated Schwartz models. In order to compare the performance of our new formulae with the performance of current popular formulae, we calibrate market prices of short tenor heating oil crack spread call options (traded on the New York Mercantile Exchange) and empirically test their performances. Results from the analysis show that our univariate-based CEV formulae outperforms known univariate formulae in capturing market prices. Overall, however we found the explicit approach to be superior to the univariate approach and in particular our new explicit-based formulae performed best in capturing market prices for options with short tenor.