Vol.124, No.2, 2020, pp.493-508, doi:10.32604/cmes.2020.010208
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ARTICLE
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: ljodar@mat.upv.es
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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