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Pricing American Stock Options by Linear Programming

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  • M. A. H. Dempster
  • J. P. Hutton
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    Abstract

    We investigate numerical solution of finite difference approximations to American option pricing problems, using a new direct numerical method: simplex solution of a linear programming formulation. This approach is based on an extension to the parabolic case of the equivalence between linear order complementarity problems and abstract linear programs known for certain elliptic operators. We test this method empirically, comparing simplex and interior point algorithms with the projected successive overrelaxation (PSOR) algorithm applied to the American vanilla and lookback puts. We conclude that simplex is roughly comparable with projected SOR on average (faster for fine discretizations, slower for coarse), but is more desirable for robustness of solution time under changes in parameters. Furthermore, significant speedups over the results given here have been achieved and will be published elsewhere. Copyright Blackwell Publishers Inc 1999.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 9 (1999)
    Issue (Month): 3 ()
    Pages: 229-254

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    Handle: RePEc:bla:mathfi:v:9:y:1999:i:3:p:229-254

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    Cited by:
    1. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Discussion Paper 2004-19, Tilburg University, Center for Economic Research.
    2. Valeriy Ryabchenko & Sergey Sarykalin & Stan Uryasev, 2004. "Pricing European Options by Numerical Replication: Quadratic Programming with Constraints," Asia-Pacific Financial Markets, Springer, vol. 11(3), pages 301-333, September.
    3. Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.
    4. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
    5. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
    6. Yoshifumi Muroi & Takashi Yamada, 2008. "An Explicit Finite Difference Approach to the Pricing Problems of Perpetual Bermudan Options," Asia-Pacific Financial Markets, Springer, vol. 15(3), pages 229-253, December.
    7. Yoshifumi Muroi & Takashi Yamada, 2006. "Pricing problems of perpetual Bermudan options," Computing in Economics and Finance 2006 345, Society for Computational Economics.
    8. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.

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