Perpetual Barrier Options in Jump-Diffusion Models
AbstractWe present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial irregular optimal stopping problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The obtained solution of the nontrivial free-boundary problem gives the possibility to observe some special analytic properties of the value function at the optimal stopping boundaries.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-058.
Length: 24 pages
Date of creation: Sep 2006
Date of revision:
American double barrier options; optimal stopping problem; jump-diffusion model; integro-differential free-boundary problem; continuous and smooth fit; Ito-Tanaka-Meyer formula;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Rama Cont & Ekaterina Voltchkova, 2005.
"Integro-differential equations for option prices in exponential Lévy models,"
Finance and Stochastics,
Springer, vol. 9(3), pages 299-325, 07.
- Cont, Rama & Voltchkova, Ekaterina, 2005. "Integro-Differential Equations for Option Prices in Exponential Lévy Models," Open Access publications from University of Toulouse 1 Capitole http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
- L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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