A Time-Dependent Variance Model for Pricing Variance and Volatility Swaps

Abstract

Abstract Analytic solutions are found for prices of variance and volatility swaps under a new time-dependent stochastic model for the dynamics of variance. The main features of the new stochastic differential equation are (1) an empirically validated cν3/2 diffusion term and (2) a free function of time as a moving target in a reversion term, allowing additional flexibility for model calibration against market data.