Open Access
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:
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
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.
Citations