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Integral Options in Models with Jumps

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  • Pavel V. Gapeev

Abstract

We present an explicit solution to the formulated in [17] optimal stopping problem for a geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the smooth fit may break down and then be replaced by the continuous fit. The result can be interpreted as pricing perpetual integral options in a model with jumps.

Suggested Citation

  • Pavel V. Gapeev, 2006. "Integral Options in Models with Jumps," SFB 649 Discussion Papers SFB649DP2006-068, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-068
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-068.pdf
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    References listed on IDEAS

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    1. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    2. Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
    3. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    4. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    5. Gapeev, P.V. & Peskir, G., 2006. "The Wiener disorder problem with finite horizon," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1770-1791, December.
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    More about this item

    Keywords

    Jump process; stochastic differential equation; optimal stopping problem; integral American option; compound Poisson process; Shiryaev´s process; Girsanov´s theorem; Ito´s formula; integrodifferential free-boundary problem; smooth and continuous fit; hypergeometric functions;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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