Regularity of the free boundary of an American option on several assets

Abstract

Abstract We establish the C ∞ regularity of the free boundary for an American option on several assets in the case where the payoff is convex and the assets follow correlated geometric Brownian motions. Our work builds on results concerning the qualitative properties and initial regularity of the free boundary by Broadie and Detemple; Jaillet, Lamberton, and Lapeyre; and Villeneuve. © 2008 Wiley Periodicals, Inc.