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. Under general stochastic volatility dynamics, we analyze the discretization effect and obtain an analytical correction term to be applied to the value of options on continuously sampled variance. The result allows for a straightforward implementation in many of the standard stochastic volatility models proposed in the literature. Finally, we compare the performance of different numerical methods for pricing options on discretely sampled variance and give recommendations based on the option’s characteristics.

Keywords: options on realized variance, variance swaps, stochastic volatility, discrete sampling, numerical pricing methods