On the American Option Value Near its Exercise Region.

American options valuation leads to solve an optimal stopping problem or a variational inequality. These two approaches involve the knowledge of a free boundary, boundary of the so-called exercise region. Numerical methods exist to solve this kind of problems but these methods are not very efficient in high dimension because some information on the free boundary is needed. To improve our knowledge of the value function near its exercise region, we give here a lower bound for the difference between the value function and the pay-off function near the free boundary. This result can be used, for instance, to get some estimation for the convergence rate of the Bermudean option exercise region to the American one. [ABSTRACT FROM AUTHOR]