Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives
We use dynamic programming, finite elements, and parallel computing to design and evaluate two-dimensional financial derivatives. Our dynamic program is flexible, as it divides the evaluation process into two components: one related to the dynamics of the underlying process and the other to the char...
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MDPI AG
2024-11-01
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| author | Malek Ben-Abdellatif Hatem Ben-Ameur Rim Chérif Bruno Rémillard |
| author_facet | Malek Ben-Abdellatif Hatem Ben-Ameur Rim Chérif Bruno Rémillard |
| author_sort | Malek Ben-Abdellatif |
| collection | DOAJ |
| description | We use dynamic programming, finite elements, and parallel computing to design and evaluate two-dimensional financial derivatives. Our dynamic program is flexible, as it divides the evaluation process into two components: one related to the dynamics of the underlying process and the other to the characteristics of the financial derivative. It is efficient as it uses local polynomials at each step of the backward recursion to approximate the option value function, while it assumes only a numerical (but not a statistical) error and a state (but not a time) discretization. Parallel computing is used to speed up the model resolution and enhance its overall efficiency. To support our construction, we evaluate American options, which are subject to market risk, and exchangeable bonds, which are subject to default risk. |
| format | Article |
| id | doaj-art-a4b76fa394484b23b43c855e3b7f207b |
| institution | OA Journals |
| issn | 2227-9091 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Risks |
| spelling | doaj-art-a4b76fa394484b23b43c855e3b7f207b2025-08-20T02:01:09ZengMDPI AGRisks2227-90912024-11-01121218310.3390/risks12120183Dynamic Programming for Designing and Valuing Two-Dimensional Financial DerivativesMalek Ben-Abdellatif0Hatem Ben-Ameur1Rim Chérif2Bruno Rémillard3Department of Finance, School of Business, ESLSCA University, Giza 12511, EgyptDepartment of Decision Sciences, HEC Montréal, Montréal, QC H3T 2A7, CanadaDepartment of Management, School of Business, The American University of Cairo, New Cairo 11835, EgyptDepartment of Decision Sciences, HEC Montréal, Montréal, QC H3T 2A7, CanadaWe use dynamic programming, finite elements, and parallel computing to design and evaluate two-dimensional financial derivatives. Our dynamic program is flexible, as it divides the evaluation process into two components: one related to the dynamics of the underlying process and the other to the characteristics of the financial derivative. It is efficient as it uses local polynomials at each step of the backward recursion to approximate the option value function, while it assumes only a numerical (but not a statistical) error and a state (but not a time) discretization. Parallel computing is used to speed up the model resolution and enhance its overall efficiency. To support our construction, we evaluate American options, which are subject to market risk, and exchangeable bonds, which are subject to default risk.https://www.mdpi.com/2227-9091/12/12/183dynamic programmingfinite elementsparallel computingtwo-dimensional American optionsexchangeable bonds |
| spellingShingle | Malek Ben-Abdellatif Hatem Ben-Ameur Rim Chérif Bruno Rémillard Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives Risks dynamic programming finite elements parallel computing two-dimensional American options exchangeable bonds |
| title | Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives |
| title_full | Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives |
| title_fullStr | Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives |
| title_full_unstemmed | Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives |
| title_short | Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives |
| title_sort | dynamic programming for designing and valuing two dimensional financial derivatives |
| topic | dynamic programming finite elements parallel computing two-dimensional American options exchangeable bonds |
| url | https://www.mdpi.com/2227-9091/12/12/183 |
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