Multivariate Variance Swap Using Generalized Variance Method for Stochastic Volatility models

Paper: arXiv 2510.20047

Authors: Semere Gebresilassie, Mulue Gebreslasie, Minglian Lin

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a mathematically solid derivation for pricing multivariate variance swaps using the determinant of the covariance matrix under Heston and BNS stochastic volatility models. However, its empirical rigor is limited, relying primarily on simulated data from nine assets via R packages rather than exhaustive real-world backtesting and execution analysis.

Research Flowchart

  flowchart TD
    A[Goal: Value Multi-Asset Variance Swaps via Generalized Variance] --> B[Framework: Heston & BNS Stochastic Volatility Models]
    B --> C[Inputs: 9 Assets Data via quantmod Package]
    C --> D[Derive Closed-Form Solutions for 3-Asset Portfolio]
    D --> E[Simulations, Parameter Testing & Model Calibration]
    E --> F[Outcome: Robust Framework & Exact Formulas for Multivariate Swaps]