The Closed-form Solution for Pricing American Put Options

Wang Xiaodong

This paper proposes a closed-form solution for pricing an American put
option on a non-dividend paying stock based on an optimally early-exercise strategy. An American put option should be early-exercised when the maximum option premium of early exercise is not less than the value of its European counterpart; otherwise, it should not be early-exercised. This paper also shows that Merton (1973)’s formula for pricing a perpetual American put option on a non-dividend paying stock is not perfect and shows such an option’s value is equal to its strike price.