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Volume 13, Issue 6
An ADI Sparse Grid Method for Pricing Efficiently American Options under the Heston Model

A. Clevenhaus, M. Ehrhardt & M. Günther

Adv. Appl. Math. Mech., 13 (2021), pp. 1384-1397.

Published online: 2021-08

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  • 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.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1384, author = {Clevenhaus , A.Ehrhardt , M. and Günther , M.}, title = {An ADI Sparse Grid Method for Pricing Efficiently American Options under the Heston Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0317}, url = {http://global-sci.org/intro/article_detail/aamm/19427.html} }
TY - JOUR T1 - An ADI Sparse Grid Method for Pricing Efficiently American Options under the Heston Model AU - Clevenhaus , A. AU - Ehrhardt , M. AU - Günther , M. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1384 EP - 1397 PY - 2021 DA - 2021/08 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0317 UR - https://global-sci.org/intro/article_detail/aamm/19427.html KW - Sparse grid, combination technique, American options, ADI, Heston model. AB -

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.

A. Clevenhaus, M. Ehrhardt & M. Günther. (1970). An ADI Sparse Grid Method for Pricing Efficiently American Options under the Heston Model. Advances in Applied Mathematics and Mechanics. 13 (6). 1384-1397. doi:10.4208/aamm.OA-2020-0317
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