Perpetual barrier options in jump-diffusion models

Pavel V. Gapeev

No 2006-058, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We present a closed form solution to the perpetual American double barrier call option problem in a model driven by Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the inital 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.

Keywords: American double barrier options; optimal stopping problem; jump-diffusion model; integro-differential free-boundary problem; continuous and smooth fit; It^o-Tanaka-Meyer formula (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2006
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