Perpetual barrier options in jump-diffusion models - Pavel V. Gapeev (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2006)
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: G13; 330; American double barrier options; optimal stopping problem; jump-diffusion model; integro-differential free-boundary problem; continuous and smooth fit; It^o-Tanaka-Meyer formula