On pricing variance swaps in discretely-sampled with High Volatility model

Abstract

In this paper, the valuation of discretely sampled variance swaps is investigated in a financial asset price model with an increase in volatility. More precisely, we consider a stochastic differential equation model with an additional parameter that augments volatility. This is to cover the impact of financial crunches on the prices of a given asset. Under these settings, the calculation of the annualized delivery price of a variance swap is not sure in a closed-form. Following the literature, the delivery price can be written as a finite sum of conditional expectations. We focus our attention on the computations of these expectations and we obtain some interesting results. This leads to a semi- analytical solution to the variance swaps pricing problems. Some illustrations showing the goodness of our model are provided.