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An Analysis of Path-Dependent Options

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  • Frank Wusterhausen

    (Martin Luther University Halle-Wittenberg)

Abstract

The objective of this paper is to provide an analytic theory for pricing path-dependent options of European type. General conditions for the path-dependencies are introduced, which allow a wide range of application. We present a partial differential equation describing the fair price process of a path-dependent option in a Black–Scholes world, where the classical Black–Scholes equation involves additional terms caused by the path-dependency of the option. The main result is that the problem is well posed in appropriate function spaces.

Suggested Citation

  • Frank Wusterhausen, 2015. "An Analysis of Path-Dependent Options," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 874-887, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0405-6
    DOI: 10.1007/s10957-013-0405-6
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    References listed on IDEAS

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    1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    2. Piergiacomo Sabino, 2009. "Efficient quasi-Monte simulations for pricing high-dimensional path-dependent options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 49-65, May.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
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    Cited by:

    1. Juhasz, Peter & Varadi, Kata & Vidovics-Dancs, Agnes & Szaz, Janos, 2017. "Measuring Path Dependency," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 8(1), pages 29-37.

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