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Approximation of Dynamic Programs

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Handbook of Computational Finance

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

Under some standard market assumptions, evaluating a derivative implies computing the discounted expected value of its future cash flows and can be written as a stochastic Dynamic Program (DP), where the state variable corresponds to the underlying assets’ observable characteristics. Approximation procedures are needed to discretize the state space and to reduce the computational burden of the DP algorithm. One possible approach consists in interpolating the function representing the value of the derivative using polynomial basis functions. This chapter presents basic interpolation approaches used in DP algorithms for the evaluation of financial options, in the simple setting of a Bermudian put option.

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References

  • Ben Abdallah, R., Ben-Ameur, H., & Breton, M. (2009). An analysis of the true notional bond system applied to the CBOT T-Bond futures. Journal of Banking and Finance, 33, 534–545.

    Article  Google Scholar 

  • Ben-Ameur, H., Breton, M., & l’Écuyer, P. (2002). A dynamic programming procedure for pricing American-style Asian options. Management Science, 48, 625–643.

    Google Scholar 

  • Ben-Ameur, H., Breton, M., & François, P. (2006). A dynamic programming approach to price installment options. European Journal of Operational Research, 169(2), 667–676.

    Article  MathSciNet  MATH  Google Scholar 

  • Ben-Ameur, H., Breton, M., Karoui, L., & L’Écuyer, P. (2007). A dynamic programming approach for pricing options embedded in bonds. Journal of Economic Dynamics and Control, 31, 2212–2233.

    Article  MathSciNet  MATH  Google Scholar 

  • Ben-Ameur, H., Breton, M., & Martinez, J. (2009). Dynamic programming approach for valuing options in the GARCH model. Management Science, 55(2), 252–266.

    Article  MATH  Google Scholar 

  • Breton, M., & de Frutos, J. (2010). Option pricing under GARCH processes by PDE methods. Operations Research, 58, 1148–1157.

    Article  MathSciNet  MATH  Google Scholar 

  • Breton, M., de Frutos, J., & Serghini-Idrissi, S. (2010). Pricing options under GARCH in a dynamic programming spectral approximation framework, GERAD working paper.

    Google Scholar 

  • Canuto, C., Hussaini, M. Y., Quarteroni, A., & Zang, T. A. (2006). Spectral methods. Fundamentals in single domains. Heidelberg: Springer.

    Google Scholar 

  • Chiarella, C., El-Hassan, N., & Kucera, A. (1999). Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansion. Journal of Economic Dynamics and Control, 23(9–10), 1387–1424.

    Article  MathSciNet  MATH  Google Scholar 

  • Chiarella, C., El-Hassan, N., & Kucera, A. (2008a). The evaluation of discrete barrier options in a path integral framework. In E. Kontoghiorghes, B. Rustem & P. Winker (Eds.), Computational methods in financial engineering: essays in honour of Manfred Gilli (pp. 117–144). Heidelberg: Springer.

    Chapter  Google Scholar 

  • Chiarella, C., Meyer, G., & Ziogas, A. (2008b). Pricing american options under stochastic volatility and jump-diffusion dynamics. In K. Muller & U. Steffens (Eds.), Die Zukunft der Finanzdienstleistungs-industrie in Deutschland (pp. 213–236). Germany: Frankfurt School.

    Google Scholar 

  • Duan, J. C., & Simonato, J. G. (2001). American option pricing under GARCH by a Markov chain approximation. Journal of Economic Dynamics and Control, 25, 1689–1718.

    Article  MathSciNet  MATH  Google Scholar 

  • de Frutos, J. (2008). A spectral method for bonds. Computers and Operations Research, 35, 64–75.

    Article  MathSciNet  MATH  Google Scholar 

  • Whitt, W. (1978). Approximation of dynamic programs I. Mathematics of Operations Research, 3, 231–243.

    Article  MathSciNet  MATH  Google Scholar 

  • Whitt, W. (1979). Approximation of dynamic programs II. Mathematics of Operations Research, 4, 179–185.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Research supported by IFM2 and by NSERC (Canada) to the first author, and Spanish MICINN, grant MTM2007-60528 (co-financed by FEDER funds) to the second author.

Author information

Authors and Affiliations

  1. GERAD, HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, QC, Canada, H3T 2A7

    Michèle Breton

  2. GERAD and Dpto de Matemática Aplicada, Universidad de Valladolid, Valladolid, Spain

    Javier de Frutos

Authors
  1. Michèle Breton
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  2. Javier de Frutos
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Corresponding author

Correspondence to Michèle Breton .

Editor information

Editors and Affiliations

  1. , Risk Management Institute, National University of Singapore, 21 Heng Mui Keng Terrace, Level 4, Singapore, 119613, Singapore

    Jin-Chuan Duan

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. , Department of Computational and Data Sci, George Mason University, University Drive 4400, Fairfax, 22030, Virginia, USA

    James E. Gentle

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Breton, M., de Frutos, J. (2012). Approximation of Dynamic Programs. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_23

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