THE FEYNMAN–KAC FORMULA AND PRICING OCCUPATION TIME DERIVATIVES

Julien Hugonnier

International Journal of Theoretical and Applied Finance (IJTAF), 1999, vol. 02, issue 02, 153-178

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.

Keywords: Occupation times; Path dependent options; Feynman–Kac formula; Laplace transform; Hedge ratio (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S021902499900011X

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