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Scale invariance and contingent claim pricing II: Path-dependent contingent claims

Author

Listed:
  • Jiri Hoogland

    (CWI, Amsterdam)

  • Dimitri Neumann

    (CWI, Amsterdam)

Abstract

This article is the second one in a series on the use of scaling invariance in finance. In the first paper, we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects only, and which completely avoids the use of martingale techniques. In this article we show the use of the formalism in the context of path-dependent options. We derive compact and intuitive formulae for the prices of a whole range of well known options such as arithmetic and geometric average options, barriers, rebates and lookback options. Some of these have not appeared in the literature before. For example, we find rather elegant formulae for double barrier options with moving barriers, continuous dividends and all possible configurations of the barriers. The strength of the formalism reveals itself in the ease with which these prices can be derived. This allowed us to pinpoint some mistakes regarding geometric mean options, which frequently appear in the literature. Furthermore, symmetries such as put-call transformations appear in a natural way within the framework.

Suggested Citation

  • Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing II: Path-dependent contingent claims," Finance 9907003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:9907003
    Note: Type of Document - PDF; prepared on NT/Latex; to print on PDF printer; pages: 20 . See also http://www.cwi.nl/~jiri for postscript version
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    References listed on IDEAS

    as
    1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    2. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    3. 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.
    4. Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, University Library of Munich, Germany.
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    Cited by:

    1. Jiri Hoogland & Dimitri Neumann, 2001. "Tradable Schemes," Finance 0105003, University Library of Munich, Germany.
    2. Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, University Library of Munich, Germany.
    3. Jiri Hoogland & Dimitri Neumann, 2001. "Asians and cash dividends: Exploiting symmetries in pricing theory," Finance 0105002, University Library of Munich, Germany.

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    More about this item

    Keywords

    contingent claim pricing; scale-invariance; homogeneity; 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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