Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes

Abstract

The main goal of this paper is to model variance and volatility swap using superposition of Barndorff-Nielsen and Shephard (BN-S) type models. In particular, in this paper we propose superposition of Levy process driven by Γ(ν,α) and Inverse Gaussian distributions. Model performance is assessed on data not used to build the model (i.e., test data). It is shown that the prediction error rate for the models considered in this paper are much lower compared to those from previous related models. Moreover, it is shown that unlike previous related models which are restricted to stable markets, the present approach can be applied to both stable and unstable markets.