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A Dynamic Programming Procedure for Pricing American-Style Asian Options

Author

Listed:
  • Hatem Ben-Ameur

    (GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7)

  • Michèle Breton

    (GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7)

  • Pierre L'Ecuyer

    (GERAD and Département d'Informatique et de Recherche Opérationnelle Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Canada H3C 3J7 http://www.iro.umontreal.ca/~lecuyer)

Abstract

Pricing European-style Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no easily computable analytical solution is available. Pricing their American-style counterparts, which provide early exercise opportunities, poses the additional difficulty of solving a dynamic optimization problem to determine the optimal exercise strategy. A procedure for pricing American-style Asian options of the Bermudan flavor, based on dynamic programming combined with finite-element piecewise-polynomial approximation of the value function, is developed here. A convergence proof is provided. Numerical experiments illustrate the consistency and efficiency of the PROCEDURE. Theoretical properties of the value function and of the optimal exercise strategy are also established.

Suggested Citation

  • Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:5:p:625-643
    DOI: 10.1287/mnsc.48.5.625.7803
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    References listed on IDEAS

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    Cited by:

    1. Ben-Ameur, Hatem & de Frutos, Javier & Fakhfakh, Tarek & Diaby, Vacaba, 2013. "Upper and lower bounds for convex value functions of derivative contracts," Economic Modelling, Elsevier, vol. 34(C), pages 69-75.
    2. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82, January.
    3. Scott B. Laprise & Michael C. Fu & Steven I. Marcus & Andrew E. B. Lim & Huiju Zhang, 2006. "Pricing American-Style Derivatives with European Call Options," Management Science, INFORMS, vol. 52(1), pages 95-110, January.
    4. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    5. Rongwen Wu & Michael C. Fu, 2003. "Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options," Operations Research, INFORMS, vol. 51(1), pages 52-66, February.
    6. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    7. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    8. Xiaobai Zhu & Mary Hardy & David Saunders, 2017. "Valuation of a Bermudan DB underpin hybrid pension benefit," Papers 1708.04281, arXiv.org.
    9. Hatem Ben-Ameur & Michèle Breton & Juan-Manuel Martinez, 2009. "Dynamic Programming Approach for Valuing Options in the GARCH Model," Management Science, INFORMS, vol. 55(2), pages 252-266, February.
    10. Noorani, Idin & Mehrdoust, Farshid & Nasroallah, Abdelaziz, 2021. "A generalized antithetic variates Monte-Carlo simulation method for pricing of Asian option in a Markov regime-switching model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 1-15.
    11. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.
    12. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.
    13. Ben-Ameur, Hatem & Breton, Michele & Francois, Pascal, 2006. "A dynamic programming approach to price installment options," European Journal of Operational Research, Elsevier, vol. 169(2), pages 667-676, March.

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