American option: an optimal stopping problem

Abstract

We show that the problem of pricing the perpetual American options can be treated as an optimal stopping problem. We impose some boundary conditions to arrive at the optimal solutions. We consider the option price, stopping time, strike price and volatility to approach the problem. From the solution, we deduced that the optimal arbitrage free price for the perpetual American put option can only be determined if the optimal value of the stock price of the option is known.