| Applying variational inequality technique we analyze the behavior of freeboundary of American-style interest rate option under the assumption that the in-terest rates obey a mean-reverting random walk as given by the Vasicek model. Firstwe obtain the lower bound of the free boundary, then transform the free boundaryproblem to a variational inequality, we introduce a penalty function and provethe existence and uniqueness of the solution of the variational inequality. Last themonotonicity, boundedness and C~∞-smoothness of free boundary will be proved inthis paper. |
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