Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : We consider a complete market which rules out arbitrage. In the BlackScholes model with local volatility the pricing of American
option yields a parabolic obstacle problem. This paper is devoted to local
regularity results of the exercise boundary for an
American option on one underlying asset. We give an energy and a density criterion to
characterise the subsets of the exercise boundary which are HÃ¶lder continuous with exponent
1/2. As an illustration we apply these results to the
generalised BlackScholes model where the volatility and the interest
rate do not depend
on time. In this case we prove
that the exercise boundary of the American put and call options
are HÃ¶lder continuous with exponent 1/2. 





200539 

20072005 

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