Optimal stopping and perpetual options for Lévy processes
AbstractConsider 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.
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Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 6 (2002)
Issue (Month): 4 ()
Note: received: June 2000; final version received: November 2001
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Web page: http://www.springerlink.com/content/101164/
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- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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