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A Dynamic Programming Approach for Pricing Options Embedded in Bonds

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  • Hatem Ben-Ameur
  • Michèle Breton

Abstract

The aim of this paper is to price options embedded in bonds in a Dynamic Programming (DP) framework, the focus being on call and put options with advance notice. The pricing of interest rate derivatives was usually done via trees or finite differences. Trees are not really very efficient as they deform crudely the dynamic of the underlying asset(s), here the short term risk-free interest rate. They can be interpreted as elementary DP procedures with fixed grid sizes. For a long time, finite differences presented poor accuracy because of the discontinuities of the bond's value that may arise at decision dates. Recently, remedies were given by d'Halluin et al (2001) via techniques related to flux limiters. DP does not suffer from discontinuities that may arise at decision dates and does not require a time discretization. It may also be implemented in discrete-time models. Results show efficiency and robustness. Suggestions to combine DP and finite differences are also formulated

Suggested Citation

  • Hatem Ben-Ameur & Michèle Breton, 2004. "A Dynamic Programming Approach for Pricing Options Embedded in Bonds," Computing in Economics and Finance 2004 237, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:237
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    Cited by:

    1. Hatem Ben-Ameur & Damiano Brigo & Eymen Errais, 2009. "A dynamic programming approach for pricing CDS and CDS options," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 717-726.
    2. Piergiacomo Sabino, 2022. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein–Uhlenbeck Type," Risks, MDPI, vol. 10(8), pages 1-23, July.
    3. Feng Dong & Nicola Chiara & Jan Vecer, 2010. "Valuing Callable And Putable Revenue-Performance-Linked Project Backed Securities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 751-765.

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    More about this item

    Keywords

    Dynamic Programming; Stochastic Processes; Options Embedded in Bonds; American Options;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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