Question

Consider the following data for a two-period binomial model.

The stock’s price S is $100. After three months, it either goes up and gets multiplied by the factor U = 1.138473, or it goes down and gets multiplied by the factor D = 0.886643.

Options mature after T = 0.5 year and have a strike price of K = $110.

The continuously compounded risk-free interest rate r is 5 percent per year.

Today’s European call price is c and the put price is p. Call prices after one period are denoted by c_Uin the up node and c_Din the down node. Call prices after two periods are denoted by c_UDin the “up, and then down node” and so on. Put prices are similarly defined.

Calculate American put prices in the two-period tree.   

[Note: American call tree same as European call tree (due to absence of dividends)]

Answer 1

The put option price will be 13.02 using the below parameters as mentioned in the question.

​​​