Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives

Malek Ben-Abdellatif (), Hatem Ben-Ameur, Rim Chérif and Bruno Rémillard
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Malek Ben-Abdellatif: Department of Finance, School of Business, ESLSCA University, Giza 12511, Egypt
Hatem Ben-Ameur: Department of Decision Sciences, HEC Montréal, Montréal, QC H3T 2A7, Canada
Rim Chérif: Department of Management, School of Business, The American University of Cairo, New Cairo 11835, Egypt
Bruno Rémillard: Department of Decision Sciences, HEC Montréal, Montréal, QC H3T 2A7, Canada

Risks, 2024, vol. 12, issue 12, 1-15

Abstract: 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.

Keywords: dynamic programming; finite elements; parallel computing; two-dimensional American options; exchangeable bonds (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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