University of Illinois at Urbana-Champaign - Department of Finance

Spread options are options whose payoff is based on the difference in the prices of two underlying assets. The price of a spread option is the (discounted) double integral of the option payoffs over the risk-neutral joint distribution of the terminal prices of the two underlying assets. Analytic expressions for the values of spread puts and calls in a Black-Scholes environment are not known, and various numerical algorithms must be used. This article presents an accurate and efficient approach for pricing European-style spread options on equities, foreign currencies, and commodities. The key to the approach is to recognize that the joint density of the terminal prices of the underlying assets can be factored into the product of univariate marginal and conditional densities, and that an analytic expression for the integral of the option payoffs over the conditional density is available. The remaining integration amounts to valuing the payoff function given by the results of the first integration. This payoff function is approximated by a portfolio of ordinary puts and calls, and valued accordingly.The approach is more accurate than existing bivariate binomial schemes, and fast enough for practical applications. It also allows for accurate and efficient computation of the partial derivatives of the option price, i.e., the Greek letter risks.