A correlated Heston’s stochastic volatility model: A binomial tree approach

This paper proposes a correlated binomial tree approach to model the Heston stochas-tic volatility process. The construction preserves the instantaneous correlation between the asset and volatility processes within a strictly recombining binomial framework. The Heston model is utilized for its ability to capture the dynamics of stochastic volatility, offering a more realistic representation of market behavior. The proposed approach improves upon existing tree-based models by incorporating the intrinsic correlation between the asset price and volatility processes, which is a key aspect of the original Heston model. Additionally, unlike Monte Carlo method, which rely on the random sampling and yield random outcomes, this approach is non-stochastic and yields convergent results with respect to the discretization of the tree. This allows for more stable and consistent parameter fitting when applied to real-world data, providing a reliable estimation of model parameters. An additional as-sumption that volatility remains constant during each transition is introduced, under which it is proven that the tree approach converges in distribution to the continuous Heston model under this assumption. Numerical experiments, and empirical evidence from the China Securities Index 300 option market further demonstrate the robustness and practical applicability of the proposed approach, showing that it can serve as a reliable tool for both option pricing and volatility modeling in practice.