Analytic Approximations for Spread Options

Abstract

This paper expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new analytic approximation for the price of a European spread option, and a corresponding approximation for each of its price, volatilty and correlation hedge ratios. Our approach has many advantages over existing analytic approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur carry costs. Simulations quantify the accuracy of our approach; we also present an empirical application, to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996) which is commonly used by traders.Spread options, exchange options, American options, analytic formula, Kirks approximation, correlation skew