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On the efficient application of the repeated Richardson extrapolation technique to option pricing

Author

Listed:
  • Luca Barzanti

    (University of Bologna)

  • Corrado Corradi

    (University of Bologna)

  • Martina Nardon

    (Department of Applied Mathematics, University of Venice)

Abstract

Richardson extrapolation (RE) is a commonly used technique in financial applications for accelerating the convergence of numerical methods. Particularly in option pricing, it is possible to refine the results of several approaches by applying RE, in order to avoid the difficulties of employing slowly converging schemes. But the effectiveness of such a technique is fully achieved when its repeated version (RRE) is applied. Nevertheless, its application in financial literature is pretty rare. This is probably due to the necessity to pay special attention to the numerical aspects of its implementation, such as the choice of both the sequence of the stepsizes and the order of the method. In this contribution, we consider several numerical schemes for the valuation of American options and investigate the possibility of an appropriate application of RRE. As a result, we find that, in the analyzed approaches in which the convergence is monotonic, RRE can be used as an effective tool for improving significantly the accuracy.

Suggested Citation

  • Luca Barzanti & Corrado Corradi & Martina Nardon, 2006. "On the efficient application of the repeated Richardson extrapolation technique to option pricing," Working Papers 147, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpaper:147
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    References listed on IDEAS

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    1. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    2. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-840, June.
    3. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(2), pages 153-164, June.
    4. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    5. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    6. Steve Heston & Guofu Zhou, 2000. "On the Rate of Convergence of Discrete‐Time Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 53-75, January.
    7. Omberg, Edward, 1987. "A Note on the Convergence of Binomial-Pricing and Compound-Option," Journal of Finance, American Finance Association, vol. 42(2), pages 463-469, June.
    8. Bunch, David S & Johnson, Herb, 1992. "A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-816, June.
    9. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
    10. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    12. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    13. Dietmar P. J. Leisen, "undated". "The Random-Time Binomial Model," Computing in Economics and Finance 1997 82, Society for Computational Economics.
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    More about this item

    Keywords

    Richardson extrapolation; repeated Richardson extrapolation; American options; randomization technique; flexible binomial method;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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