Regularity of the free boundary of American options
by Lee, Youngseok, Ph.D., NEW YORK UNIVERSITY, 2011, 74 pages; 3466920

Abstract:

We introduce pricing of American options on several assets that follow a geometric Brownian motion as a free boundary problem. A crucial assumption is that payoff functions are smooth in the region where the option is exercised. This assumption is true for various options traded in the derivatives market. A key ingredient for analysis of the free boundary is a monotonicity formula. Existence and uniqueness of homogeneous blow-up limits at a fixed point on the free boundary are guaranteed by the monotonicity formula. Then the free boundary can be classified into high energy points and low energy points by nondegeneracy of the solution. The time projection of the set of high energy point is analyzed measure theoretically. We prove that the set of low energy points is locally space-time C1,α. Finally, we can obtain C1,α regularity of the free boundary for some particular payoff functions.
 
AdviserFanghua Lin
SchoolNEW YORK UNIVERSITY
SourceDAI/B 72-10, p. , Aug 2011
Source TypeDissertation
SubjectsApplied mathematics; Mathematics; Finance
Publication Number3466920
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