Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change

Abstract

We propose a new class of models for pricing generalized variance swaps. We assume that, in the most general form, the process for the asset price is a function of a general time-homogeneous diffusion process belonging to a symmetric pricing semigroup, time changed by a composition of a Lévy subordinator and an absolutely continuous process. We derive the analytical pricing formulas for various types of generalized variance swaps based on eigenfunction expansion method. We also numerically implement the model and test its sensitivity to some of the key parameters of the model.