The American put is log-concave in the log-price

We show that the American put option price is log-concave as a function of the log-price of the underlying asset. Thus the elasticity of the price decreases with increasing stock value. We also consider related contracts of American type, and we provide an example showing that not all American option prices are log-concave in the stock log-price.  2005 Elsevier Inc. All rights reserved