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Fast numerical valuation of American, exotic and complex options

Author

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

Abstract

The purpose of this paper is to present evidence in support of the hypothesis that fast, accurate and parametrically robust numerical valuation of a wide range of derivative securities can be achieved by use of direct numerical methods in the solution of the associated PDE problems. Specifically, linear programming methods for American vanilla and exotic options, and explicit methods for a three stochastic state variable problem (a multi-period terminable differential swap) are explored and promising numerical results are discussed. The resulting value surface gives, simultaneously, valuation for many maturities and underlying prices, and the parameters required for risk analysis.

Suggested Citation

  • M. A. H. Dempster & J. P. Hutton, 1997. "Fast numerical valuation of American, exotic and complex options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 1-20.
    • Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:1-20
    DOI: 10.1080/135048697334809
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    References listed on IDEAS

    as
    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. J. M. Borwein & M. A. H. Dempster, 1989. "The Linear Order Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 534-558, August.
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    Cited by:

    1. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    2. Vladimir V. Piterbarg, 2004. "Risk Sensitivities Of Bermuda Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 465-509.
    3. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    4. P. A. Forsyth & K. R. Vetzal & R. Zvan, 1999. "A finite element approach to the pricing of discrete lookbacks with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(2), pages 87-106.
    5. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.

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