A note on closed-form spread option valuation under log-normal models

In the papers Carmona and Durrleman [Pricing and hedging spread options in a log-normal model. Technical report: Department of Operations Research and Financial Engineering, Princeton, NJ, Princeton University, 2003] and Bjerksund and Stensland [Closed form spread option valuation. Quant. Finance, 2014, 14(10), 1785–1794], closed-form approximations for spread call option prices were studied under the log-normal models. In this paper, we give an alternative closed-form formula for the price of spread call options under the log-normal models also. Our formula can be seen as a generalization of the closed-form formula presented in Bjerksund and Stensland [Closed form spread option valuation. Quant. Finance, 2014, 14(10), 1785–1794] as their formula can be obtained by selecting special parameter values for our formula. Numerical tests show that our formula performs better for a certain range of model parameters than the closed-form formula presented in Bjerksund and Stensland [Closed form spread option valuation. Quant. Finance, 2014, 14(10), 1785–1794].