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Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives

Author

Listed:
  • 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)

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.

Suggested Citation

  • Malek Ben-Abdellatif & Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2024. "Dynamic Programming for Designing and Valuing Two-Dimensional Financial Derivatives," Risks, MDPI, vol. 12(12), pages 1-15, November.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:12:p:183-:d:1526194
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    References listed on IDEAS

    as
    1. Ibáñez, Alfredo & Zapatero, Fernando, 2004. "Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(2), pages 253-275, June.
    2. Hamza Hanbali & Daniel Linders, 2019. "American-type basket option pricing: a simple two-dimensional partial differential equation," Quantitative Finance, Taylor & Francis Journals, vol. 19(10), pages 1689-1704, October.
    3. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
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