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2021
Journal Article
Titel

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

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.
Author(s)
Engelmann, Bernd
Ho Chi Minh City Open University, 35-37 Ho Hao Hon, Dist 1, Ho Chi Minh City, Vietnam
Koster, Frank
EnBW Trading GmbH, Durlacher Allee 93, D-76131 Karlsruhe, Germany
Oeltz, Daniel
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Zeitschrift
International journal of financial engineering
Thumbnail Image
DOI
10.1142/S2424786320500486
Language
English
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Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Tags
  • Heston stochastic loc...

  • Heston model

  • local volatility mode...

  • derivatives pricing

  • finite volume scheme

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