Multivariate Variance Swap Using Generalized Variance Method for Stochastic Volatility models

TL;DR

This paper introduces a new multivariate variance swap framework using generalized variance for multi-asset portfolios, deriving closed-form solutions under stochastic volatility models and validating through simulations.

Contribution

It develops a novel generalized variance approach for multivariate variance swaps and derives analytical solutions under Heston and BNS models.

Findings

Closed-form solutions for multivariate variance swaps under Heston and BNS models.

Simulation results validate the robustness and effectiveness of the proposed framework.

Parameter testing and calibration demonstrate practical applicability.

Abstract

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.