Valuation of Options on Discretely Sampled Variance: A General Analytic Approximation

Abstract

The values of options on realized variance are significantly impacted by the discrete sampling of realized variance and may be substantially higher than the values of options on continuously sampled variance (or, quadratic variation). Under arbitrary stochastic volatility dynamics, we analyze the discretization effect and obtain a simple analytical correction term to be applied to the value of options on continuously sampled variance. Our final result is remarkably compact and allows for a straightforward implementation in many of the standard stochastic volatility models proposed in the literature.

Keywords: options on realized variance, variance swaps, stochastic volatility, Monte Carlo

JEL Classification: C63, G13