Calibration of the Heston Stochastic Local Volatility Model: A Finite Volume Scheme

21 Pages Posted: 26 Apr 2011 Last revised: 9 Jun 2020

See all articles by Bernd Engelmann

Bernd Engelmann

Ho Chi Minh City Open University

Frank Koster


Daniel Oeltz


Date Written: June 08, 2020


The two most popular equity and FX derivatives pricing models in banking practice are the local volatility model and the Heston model. While the former has the appealing property that it can be calibrated exactly to any given set of arbitrage free European vanilla option prices, the latter delivers a more realistic smile dynamics. In this article we combine both modeling approaches to the Heston stochastic local volatility model. We build upon a theoretical framework that has been already developed and focus on the numerical model calibration which requires special care in the treatment of mixed derivatives and in cases where the Feller condition is not met in the Heston model leading to a singular transition density at zero volatility. We propose a finite volume scheme to calibrate the model after a suitable transformation of the model equation and demonstrate its accuracy in numerical test cases using real market data.

Keywords: Heston Stochastic Local Volatility Model, Heston Model, Local Volatility Model, Derivatives Pricing, Finite Volume Scheme

JEL Classification: G13

Suggested Citation

Engelmann, Bernd and Koster, Frank and Oeltz, Daniel, Calibration of the Heston Stochastic Local Volatility Model: A Finite Volume Scheme (June 08, 2020). Available at SSRN: or

Bernd Engelmann (Contact Author)

Ho Chi Minh City Open University ( email )

Ho Chi Minh City

Frank Koster

DGZ-DekaBank ( email )

Mainzer Landstr. 16
D-60325 Frankfurt

Daniel Oeltz

Independent ( email )

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