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The Feynman–Kac Formula And Pricing Occupation Time Derivatives

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  • JULIEN-N. HUGONNIER

    (ESSEC PhD. Program, Finance Dept., Av. B. Hirsch, 95021 Cergy Pontoise Cedex, France)

Abstract

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this end we use a formula of M. Kac to compute the joint law of Brownian motion and one of its occupation times. General pricing formulas for occupation time derivatives are established and it is shown that any occupation time derivative can be continuously hedged by a controlled portfolio of the basic securities. We further study some examples of interest including cumulative barrier options and discuss some numerical implementations.

Suggested Citation

  • Julien-N. Hugonnier, 1999. "The Feynman–Kac Formula And Pricing Occupation Time Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 153-178.
    • Handle: RePEc:wsi:ijtafx:v:02:y:1999:i:02:n:s021902499900011x
    DOI: 10.1142/S021902499900011X
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    Cited by:

    1. Valentin Tissot-Daguette, 2023. "Occupied Processes: Going with the Flow," Papers 2311.07936, arXiv.org, revised Dec 2023.

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