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Volume 16,     Number 4,     Winter 2008

 

ASYMPTOTICS OF AMERICAN BARRIER
OPTION PRICING
FANNU HU AND CHARLES KNESSL

Abstract. We consider an American up-and-out put barrier option under the Black and Scholes model. This corresponds to a moving boundary problem for a PDE. We apply singular perturbation methods to compute the moving boundary, as well as the full solution to the PDE. We analyze the problem in the limit of small ρ = 2r2, where r is the interest rate and σ is the volatility, and employ the ray method of geometrical optics and matched asymptotic expansions

 

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