Title: Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type L´evy Processes

Author(s): Indranil SenGupta, Musie Ghebremichael and Semere Habtemicael
Issue: Volume 81 Series B Part 1 Year 2019
Pages: 75 -- 92
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 L´evy 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.
Primary 60G10, 60G51; Secondary 91G70, 91G80
Keywords and phrases: Swap, Cumulants, Stochastic volatility, Ornstein- Uhlenbeck process, Superposition, Cross validation