A Closed-Form Formula for Pricing Variance Swaps on Commodities

Abstract

This paper presents an analytical approach for pricing discretely sampled variance swaps, when the underlying asset is set to be a commodity. We consider a variance swap with its realized variance, defined in terms of squared log returns of the underlying commodity, based on Schwartz’s one-factor model. Most interestingly, we show that our closed-form solution produces financially meaningful values of the fair delivery price in the parameter space. The current analytical approach would be beneficial for market practitioners who need an analytical solution for pricing variance swaps, and is based on a commodity underlying asset, which substantially reduces the computational burden by using Monte Carlo methods, and can be implemented efficiently.