Erik Ekström, David Hobson, Recovering a time-homogeneous stock price process from perpetual option prices, Annals of applied probability , 21(3), 2011, pp. 1102-1135
It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock price model which reproduces the given option prices.