Calibration of Heston Stochastic Local Volatility Model by Numerical Solution of Nonlinear Fokker-Planck Equation

Abstract

The Fokker-Planck partial differential equation is used to compute the probability density function of the Heston stochastic local volatility model. The solution of the Fokker Planck equation is required for the calibration of the leverage function, which plays an important role in the Heston stochastic local volatility model. The current study describes a numerical method for solving the nonlinear Fokker-Planck partial differential equation. The solution is demonstrated to converge to the one generated from the implied volatility surface by comparing call option prices.

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