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Dynamic Programming Approach for Valuing Options in the GARCH Model

Author

Listed:
  • Hatem Ben-Ameur

    (GERAD, Brock University and HEC Montréal, Montréal, Québec H3T 2A7, Canada)

  • Michèle Breton

    (GERAD and HEC Montréal, Montréal, Québec H3T 2A7, Canada)

  • Juan-Manuel Martinez

    (HEC Montréal, Montréal, Québec H3T 2A7, Canada)

Abstract

In this paper, we develop an efficient algorithm to value options under discrete-time GARCH processes. We propose a procedure based on dynamic programming coupled with piecewise polynomial approximation to compute the value of a given option, at all observation dates and levels of the state vector. The method can be used for the large GARCH family of models based on Gaussian innovations and may accommodate all low-dimensional European as well as American derivatives. Numerical implementations show that this method competes very advantageously with other available valuation methods.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:2:p:252-266
    DOI: 10.1287/mnsc.1080.0925
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    References listed on IDEAS

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    Cited by:

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    2. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    3. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    4. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147, Edward Elgar Publishing.

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