A closed-form pricing formula for variance swaps with mean-reverting Gaussian volatility

Abstract

Although variance swaps have become an important financial derivative to hedge against volatility risks, closed-form formulae have been developed only recently, when the realized variance is defined on discrete sample points and no continuous approximation is adopted to alleviate the mathematical difficulties associated with dealing with the discreteness of the sample data. In this paper, a new closed-form pricing formula for the value of a discretely sampled variance swap is presented under the assumption that the underlying asset prices can be described by a mean-reverting Gaussian volatility model. With the newly found analytical formula, not only can all the hedging ratios of a variance swap be analytically derived, the numerical values of the swap price can be efficiently computed as well. doi: 10.1017/S144618111400011X