- Regularity of the exercise boundary for American put options on assets with discrete dividends
- Number of pages
- Amsterdam: Faculteit Economie en Bedrijfskunde
- Document type
- Working paper
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time td during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of td, and tends to 0 as time tends to t− d with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of td. When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.