Network‐Based Stochastic Volatility Modeling for Interconnected Futures Markets

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.