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Efficient Computation of Hedging Parameters for Discretely Exercisable Options

Author

Listed:
  • Ron Kaniel

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Stathis Tompaidis

    (McCombs School of Business, University of Texas at Austin, Austin, Texas 78712)

  • Alexander Zemlianov

    (Lehman Brothers, New York, New York 10019)

Abstract

We propose an algorithm to calculate confidence intervals for the values of hedging parameters of discretely exercisable options using Monte Carlo simulation. The algorithm is based on a combination of the duality formulation of the optimal stopping problem for pricing discretely exercisable options and Monte Carlo estimation of hedging parameters for European options. We show that the width of the confidence interval for a hedging parameter decreases, with an increase in the computer budget, asymptotically at the same rate as the width of the confidence interval for the price of the option. The method can handle arbitrary payoff functions, general diffusion processes, and a large number of random factors. We also present a fast, heuristic, alternative method and use our method to evaluate its accuracy.

Suggested Citation

  • Ron Kaniel & Stathis Tompaidis & Alexander Zemlianov, 2008. "Efficient Computation of Hedging Parameters for Discretely Exercisable Options," Operations Research, INFORMS, vol. 56(4), pages 811-826, August.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:4:p:811-826
    DOI: 10.1287/opre.1080.0557
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    References listed on IDEAS

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    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    4. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    6. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    7. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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    Cited by:

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    Keywords

    finance; derivative hedging;

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