Section: New Results

American options

Participants : Benjamin Jourdain, Maxence Jeunesse, Damien Lamberton, Ayech Bouselmi.

American put option with discrete dividends.

B. Jourdain and M. Jeunesse are interested in the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays discrete dividends at known times during the lifetime of the option. The dividend amounts are deterministic functions of the asset prices just before the dividend dates. B. Jourdain and M. Jeunesse have proved continuity of the exercise boundary and smooth contact for the value function under general assumptions on the dividend functions.

American options in exponential Lévy models

D. Lamberton and his PhD student A. Bouselmi are working on American options within multi-dimensional exponential Lévy models.They also have preliminary results on the asymptotic behaviour of the exercise boundary of the American put near maturity in the one dimensional case when the limit is strictly smaller than the strike price.