Multivariate Variance Swap Using Generalized Variance Method for Stochastic Volatility models

This paper develops a novel framework for modeling the variance swap of multi-asset portfolios by employing the generalized variance approach, which utilizes the determinant of the covariance matrix of the underlying assets. By specifying the distribution of the log returns of the underlying assets under the Heston and Barndorff-Nielsen and Shephard (BNS) stochastic volatility frameworks, we derive closed-form solutions for the realized variance through the computation of the covariance generalization of multi-assets. To evaluate the robustness of the proposed model, we conduct simulations using nine different assets generated via the quantmod package. For a three-asset portfolio, analytical expressions for the multivariate variance swap are obtained under both the Heston and BNS models. Numerical experiments further demonstrate the effectiveness of the proposed model through parameter testing, calibration, and validation.