arXiv:2109.02872v1 [q-fin.PR] 7 Sep 2021 Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L´evy Motions Dongdong Hu a , Hasanjan Sayit a , Svetlozar T. Rachev b , a Department of Financial Mathematics, Xi’an Jiaotong Liverpool University, Suzhou, China b Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA August 27, 2021 Abstract The paper Borovkova et al. [4] uses the moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use the moment matching method to obtain semi-closed form formulas for the price of spread options under exponential L´evy models with mean-variance mixture. Unlike the semi-closed form formula in Caldana and Fusai [5], where spread prices were expressed by using a Fourier inversion formula that involves all the log return processes, our formula gives spread prices in terms of the mixing distribution of the log returns. Numerical tests show that our formulas give accurate spread prices also. Keywords: Spread Option · Moment Matching · Mean-Variance Mixture models · L´evy Price Dynamics JEL classification C02 · C60 · D40 1 Introduction Spread options are popular financial derivatives in fixed income, currency, commodity, and equity markets. They are used to hedge portfolios of long and short positions in the underlying assets. A spread option is a European call option on the spread of two assets. It gives the holder the right, but not the obligation, to purchase the spread of two assets at a fixed strike price. Its price is given by the following risk-neutral valuation formula Π= e −rT E Q [S 1 (T ) − S 2 (T ) − K] + , (1) where K is the strike price, S i (T ) is the price of asset i at maturity T for i =1, 2, r> 0 is the risk-free interest rate, and Q is the risk-neutral measure, see Delbaen and Schachermayer [11], 1