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Optimal stopping and perpetual options for Lévy processes

Author

Listed:
  • Ernesto Mordecki

    (Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400, Montevideo, Uruguay , URL:http://www.cmat.edu.uy/&mtilde;ordecki Manuscript)

Abstract

Consider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options involving the infimum of the after-mentioned process are obtained. As a direct application of the previous results, a Black-Scholes type formula is given. Also as a consequence, simple explicit formulas for prices of call options are obtained for a Lévy process with positive mixed-exponential and arbitrary negative jumps. In the case of put options, similar simple formulas are obtained under the condition of negative mixed-exponential and arbitrary positive jumps. Risk-neutral valuation is discussed and a simple jump-diffusion model is chosen to illustrate the results.

Suggested Citation

  • Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    • Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:473-493
    Note: received: June 2000; final version received: November 2001
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    More about this item

    Keywords

    Optimal stopping; Lévy processes; mixtures of exponential distributions; American options; jump-diffusion models;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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