VIX Option Pricing for Non-Parameter Heston Stochastic Local Volatility Model

The Heston-Dupire model is a well-established stochastic local volatility model that offers a non-parametric representation. This model is known to closely match the implied volatility surface of options observed in the market. However, due to its non-parametric local component, Monte Carlo simulation is the only viable numerical method for derivative pricing under this model. This article proposes a novel willow tree method to replace Monte Carlo simulation for pricing exotic options and VIX options under the Heston-Dupire model. We provide the convergence rate of this method and conduct several numerical experiments to demonstrate its accuracy and efficiency. Our proposed method offers an alternative numerical technique that can enhance the computational efficiency of pricing derivatives under the Heston-Dupire model.