Consider the one-dividend American put option model where the discrete dividend at time t_d is paid at the known rate λ, that is, the dividend payment is λS_td . Show that the slope of the optimal exercise boundary of the American put at time right before t_d is given by (Meyer, 2001)

where r is the riskless interest rate.

Consider the balance of the gain in interest income from the strike price and the loss in dividend over the differential time interval δt right before t_d.  

Transcribed Image Text:

lim t-ta dS* (t) dt = ·X, λ