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Tradable Schemes

Author

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  • Jiri Hoogland

    (CWI, Amsterdam)

  • Dimitri Neumann

    (CWI, Amsterdam)

Abstract

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very elegant way, due to the fact that in our tradable based formulation there appear no drift terms in the PDE. We construct a mixed scheme based on this idea and apply it to price various types of arithmetic Asian options, as well as plain vanilla options (both european and american style) on stocks paying known cash dividends. We find prices which are accurate to ~0.1% in about 10ms on a Pentium 233MHz computer and to ~0.001% in a second. The scheme can also be used for market conform pricing, by fitting it to observed option prices.

Suggested Citation

  • Jiri Hoogland & Dimitri Neumann, 2001. "Tradable Schemes," Finance 0105003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0105003
    Note: Type of Document - Acrobat PDF; prepared on NT/LaTeX; to print on PostScript; pages: 12 ; figures: None
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0105/0105003.pdf
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    References listed on IDEAS

    as
    1. Jiri Hoogland & Dimitri Neumann, 2001. "Asians and cash dividends: Exploiting symmetries in pricing theory," Finance 0105002, University Library of Munich, Germany.
    2. Jiri Hoogland & Dimitri Neumann, 2000. "Asians and cash dividends: Exploiting symmetries in pricing theory," Papers cond-mat/0006133, arXiv.org.
    3. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    4. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    5. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    6. Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, University Library of Munich, Germany.
    7. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    8. Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing II: Path-dependent contingent claims," Finance 9907003, University Library of Munich, Germany.
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    Cited by:

    1. J. K. Hoogland & C. D. D. Neumann & M. H. Vellekoop, 2003. "Symmetries In Jump-Diffusion Models With Applications In Option Pricing And Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 135-172.
    2. Jiri Hoogland & Dimitri Neumann & Michel Vellekoop, 2002. "Symmetries in Jump-Diffusion Models with Applications in Option Pricing and Credit Risk," Finance 0203001, University Library of Munich, Germany.

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    More about this item

    Keywords

    contingent claim pricing; numeric methods; asian options; cash dividend; partial differential equation;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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