On Pricing Options Under Two Stochastic Volatility Processes

From the Black-Scholes option pricing model, this work evaluates the evolution of the mathematical modelling into the double stochastic volatility model that studies the optimization performance in partial differential equation (PDE) methods. This paper focuses on the calibration and numerical methodology processes to derive the comparison of the Heston and the double Heston models to design a more efficient numerical iterative splitting method. Through Li and Huang’s iterative splitting method, the numerical results conclude that the mixed method reduces the overall computational cost and improves the convergence of the iterative process while maintaining the simplicity, flexibility and interpretability of PDE methods.