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An ETD Method for American Options under the Heston Model

Rafael Company1, Vera N. Egorova2, Lucas Jódar1,*, Ferran Fuster Valls3
1 Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, 46022, Spain
2 Depto. de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, 39005, Spain
3 Nfoque Advisory Services, Madrid, 28001, Spain
* Corresponding Author: Lucas Jódar. Email:

Computer Modeling in Engineering & Sciences 2020, 124(2), 493-508. https://doi.org/10.32604/cmes.2020.010208

Received 17 February 2020; Accepted 05 May 2020; Issue published 20 July 2020

Abstract

A numerical method for American options pricing on assets under the Heston stochastic volatility model is developed. A preliminary transformation is applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational costs. Free boundary is treated by the penalty method. Transformed nonlinear partial differential equation is solved numerically by using the method of lines. For full discretization the exponential time differencing method is used. Numerical analysis establishes the stability and positivity of the proposed method. The numerical convergence behaviour and effectiveness are investigated in extensive numerical experiments.

Keywords

Heston model; American option pricing; exponential time differencing; semi-discretization

Cite This Article

Company, R., Egorova, V. N., Jódar, L., Valls, F. F. (2020). An ETD Method for American Options under the Heston Model. CMES-Computer Modeling in Engineering & Sciences, 124(2), 493–508.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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