Question 9: Binomial trees with discrete dividends (10 points).

Intel is currently trading at $50. Over each of the next two months, Intel will either move up by 25% or down by 20%. Each month, the probability that Intel will move up is 60%. The simple monthly (and

monthly-compounded) risk-free rate is 1.00% (note: this is a monthly rate, not a yearly rate). Further, assume that in exactly one month, Intel will pay a dividend equal to 10% of the price of Intel stock at that time. For example, if the price of Intel is $45 in one month, the dividend will be $4.50.

Write out a two-month, two-period binomial tree for the stock price of Intel (i.e., one month per

branch). Write down the binomial model parameters u, d, r, p, and q. (2 points)

Use the binomial method to find the price of a two-month American call on Intel with K = 50. (2 points)

Use the binomial method to find the price of a two-month American put on Intel with K = 50. (2 points)

Use the binomial method to find the price of a European binary option which pays off $100 if the price of Intel is greater than or equal to $50 in two months, and pays off zero otherwise. (2 points)

How many shares would you purchase and how much would you borrow/lend today to replicate the European binary option in question d? What is the total cost of this replicating portfolio? (2 points)