Calibration of the Heston stochastic local volatility model: A finite volume scheme

Bernd Engelmann, Frank Koster () and Daniel Oeltz ()
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Bernd Engelmann: Ho Chi Minh City Open University, 35-37 Ho Hao Hon, Dist 1, Ho Chi Minh City, Vietnam
Frank Koster: EnBW Trading GmbH, Durlacher Allee 93, D-76131 Karlsruhe, Germany
Daniel Oeltz: Fraunhofer-Institut SCAI, Schloss Birlinghoven, D-53757 Sankt Augustin, Germany

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 01, 1-22

Abstract: 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 more realistic smile dynamics. In this paper, 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 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S2424786320500486

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