Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications

Abstract

The goal of this paper is to derive closed-form approximation formulas for the spread option value and Greeks by using double integration and investigating the exercise boundary. We have found that the straight-line approximation suggested in previous research does not perform well for curved exercise boundaries. We propose a novel approach: to integrate in a sector and find a closed-form formula expressed in terms of the bivariate normal CDF. We call it the sector formula. Numerical tests show the good accuracy of our sector formula. We demonstrate applications of the formula to the market data of calendar spread options for three major commodities, WTI, Natural Gas, and Corn, listed on the CME site as of May, April, and June 2024.