Pricing the American put using a new class of tight lower bounds

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon T. By put call parity, these bounds can be easily converted to bounds on the price of the American call option on a dividend paying stock. By numerically optimizing these bounds, we obtain tighter bounds on the option price. Our methodology simultaneously furnishes us with an (exponential) exercise strategy. We provide an extensive experimental computation, comparing with convergent binomial tree pricing methods. Our bounds deliver an accuracy comparable to a 2000 step binomial tree, with a computational cost comparable to a 400 step binomial tree.