Network-Based Stochastic Volatility Modeling for Interconnected Futures Markets

Abstract

This study introduces a novel network-based stochastic volatility model for futures markets, integrating graph theory with multivariate stochastic differential equations to capture cross-asset volatility spillovers. The model incorporates the graph Laplacian into volatility dynamics, overcoming a central limitation of traditional frameworks, such as the Heston model, which treat each asset's volatility as independent or fixed, and therefore cannot capture the topology-dependent transmission of volatility across linked markets. Theoretical properties, including positivity, stationarity, and affine pricing, are established, enabling efficient Fourier-based option pricing. Applications show that sparse, high-spillover network structures amplify volatility clustering, with kurtosis of 6–8 and elevated risk premia, whereas dense network structures stabilize volatility; we interpret these polar cases as stylized representations of emerging and developed markets, an interpretation we validate against real futures data in Appendix A. The model improves pricing accuracy by 8%–12% relative to Heston and reduces hedging variance by 10%–15%. Environmental, social, and governance integration via carbon futures nodes shows that sparse (emerging-market) networks experience 6%–8% higher energy-futures volatility following carbon-price shocks than dense (developed-market) networks (3%–4%), supporting sustainable finance and risk management applications.