The result for the pricing of extendible call and put options is generalized, using the Cox and Ross (1976) approach, to the case of an arbitrary number of extensions. Some typographical errors in the Longstaff (1990) results for the simplest case are corrected.

We derive a simple relationship between the critical stock price and the gamma of the American put. We use this relationship to derive the correct expression for the critical stock price as time to maturity goes to zero and an analytic approximation for the in-the-money American put price. We...