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Perpetual barrier options in jump-diffusion models

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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.

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Pavel V. Gapeev

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Adapt according to the presented license agreement and reference the original author.