Numerical computing for the moments of the Heston model


Keywords: Heston model, Stochastic differential equation, the Moments, Feynman-kac formula, Adomian decomposition method, Parabolic partial differential equation, Convergent series.

Abstract: The Heston model assumes that the underlying stock price follows a Black-Scholes model, but with stochastic variance that follows CIR model. This model has no general explicit solution. In this paper, by using Feynman-Kac formula and Adomian decomposition method, the moments of solution for the Heston model is computed numerically. The moments have many applications in statistics. For instance, the first moment is the mean, the second moment is the variance, the third moment is the skewness, the fourth moment is the kurtosis, and so forth. Finally, to show the simplicity and efficiency of the proposed method, numerical example is presented.

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