Question

What are the differences in valuing European put options and American put options when using the Binomial Option Pricing Model?

Answer 1

While valuing put options using a binomial tree, we make the tree such that the underlying stock can go up by some amount or down by some amount. Based on the upside which we mention by u and the downside which de mention by d, we calculate the probability p by the formula:

p = (exp(rt) -d)/(u - d)

where p is the probability of the upmove. Now that we have the upmove and downmove probability, we calculate the expected value of waiting i.e. going to the next period. So, in European options we don't have any option but to go to the next period because they can only be exercised on the expiry date i.e. the last period. But for American options we have the option of exercising it at any time. Hence, for Amercian puts, we compare the expected value calculated with the help of p above and the value (payoff) we are getting if the put is exercised right now. If the payoff we are getting right now is more than the expected value (if we chose to wait), then the American Put has the value equal to the payoff we get from exercising. But in European Puts we don't get this option of exercising at any time. There we have to get the expected value and that is the value of the put. Hence, this is the difference between valuing an American Put and a European Put by the Binoial Tree.