Year: 2021
Author: A. Clevenhaus, M. Ehrhardt, M. Günther
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1384–1397
Abstract
One goal of financial research is to determine fair prices on the financial market. As financial models and the data sets on which they are based are becoming ever larger and thus more complex, financial instruments must be further developed to adapt to the new complexity, with short runtimes and efficient use of memory space. Here we show the effects of combining known strategies and incorporating new ideas to further improve numerical techniques in computational finance.
In this paper we combine an ADI (alternating direction implicit) scheme for the temporal discretization with a sparse grid approach and the combination technique. The later approach considerably reduces the number of "spatial" grid points. The presented standard financial problem for the valuation of American options using the Heston model is chosen to illustrate the advantages of our approach, since it can easily be adapted to other more complex models.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0317
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 6 : pp. 1384–1397
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Sparse grid combination technique American options ADI Heston model.
Author Details
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Progress in Industrial Mathematics at ECMI 2021
The Parareal Algorithm and the Sparse Grid Combination Technique in the Application of the Heston Model
Clevenhaus, Anna
Ehrhardt, Matthias
Günther, Michael
2022
https://doi.org/10.1007/978-3-031-11818-0_62 [Citations: 0]