Effective Discretization Scheme for the Heston Model: Implicit Solution Based Approach

Four novel discretization schemes that built on the implicit solution of the variance, are proposed to effectively simulate the Heston model.The idea behind these schemes is fundamentally different from those of the Euler and Milstein based discretization schemes, and the so-called nearly exact simulation approaches.Numerical experiments show that these new schemes are of both accuracy and fast convergence in option pricing, and seem almost comparable to the famous quadratic exponential scheme.