Pricing Variance Swap for Multi-Asset Stochastic Volatility Models

This paper develops a novel framework for modeling variance swap of multi-asset stochastic volatility models by employing determinant-based instantaneous generalized variance. In this setting the determinant of the covariance matrix captures the joint dispersion of the multivariate log-return dynamics. By specifying the distribution of the log returns of the underlying assets under the Heston and Barndorff-Nielsen & Shephard (BNS) stochastic volatility frameworks, we obtain an analytical pricing expression for multi-asset Heston formulation, while BNS formulation is treated through a tractable approximation. 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 generalized 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.