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A ‘moving index’ method for the solution of the American options valuation problem

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  • Koulisianis, M.D
  • Papatheodorou, T.S

Abstract

We introduce a new technique for the solution of the American options valuation problem, which resembles the moving boundary behavior of the solution, and thus, we call it the ‘moving index’ (MI) method. We use the so-called linear complementarity formulation of the problem for which projected successive over relaxation (PSOR) is a leading and well-known method. We report on experimental results, which demonstrate that our MI method presents dramatic improvements over PSOR since it is several times faster for a given desired accuracy. There are also cases in which the MI method continues to perform well, while it is impossible to achieve the desired accuracy with PSOR within a decent time interval.

Suggested Citation

  • Koulisianis, M.D & Papatheodorou, T.S, 2000. "A ‘moving index’ method for the solution of the American options valuation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(4), pages 373-381.
    • Handle: RePEc:eee:matcom:v:54:y:2000:i:4:p:373-381
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    1. David S. Bates, "undated". "Testing Option Pricing Models," Rodney L. White Center for Financial Research Working Papers 14-95, Wharton School Rodney L. White Center for Financial Research.
    2. Geske, Robert & Shastri, Kuldeep, 1985. "Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(1), pages 45-71, March.
    3. 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.
    4. 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.
    5. Pantazopoulos, K N & Houstis, E N & Kortesis, S, 1998. "Front-Tracking Finite Difference Methods for the Valuation of American Options," Computational Economics, Springer;Society for Computational Economics, vol. 12(3), pages 255-273, December.
    6. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
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