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ON THE AMERICAN OPTION PROBLEM |
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| Authors: | Goran Peskir |
| Affiliation: | University of Aarhus |
| Abstract: | We show how the change-of-variable formula with local time on curves derived recently in Peskir (2002) can be used to prove that the optimal stopping boundary for the American put option can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation. This settles the question raised in Myneni (1992) and dating back to McKean (1965) . |
| Keywords: | American put option arbitrage-free price optimal stopping smooth fit geometric Brownian motion free-boundary problem nonlinear integral equation local time-space calculus curved boundary |