Pricing Discretely Sampled Variance Swaps with Cap/Floor Under Heston Stochastic Volatility Model

Abstract

Discretely sampled variance swaps with cap or floor are priced under the dynamics of the Heston stochastic volatility model by approximating the distribution of realized variance based on exact computation of its first and second moments. Accuracy of the proposed semi-analytical methodology is confirmed by comparing the results with Monte Carlo simulations. The influence of Heston parameters on mean and standard deviation of realized variance, as well as on payoff of variance swap with cap and floor, is shown. The paper presents a practical methodology for accurately pricing variance or volatility swaps with cap/floor, given the parameters of the Heston stochastic volatility model.