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 Black-Scholes 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 Hölder continuous with exponent 1/2. As an illustration we apply these results to the generalised Black-Scholes 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 Hölder continuous with exponent 1/2.
On the regularity of the exercise boundary for American options
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