The Closed-Form Solution for Pricing American Put Options

This book 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.