Question: Assume that the annualized, continuously compounded return on Ford stock is normally distributed with mean 0.18 and standard deviation 0.4. In addition, the annualized, continuously

Assume that the annualized, continuously compounded return on Ford stock is normally distributed with mean 0.18 and standard deviation 0.4. In addition, the annualized, continuously compounded risk-free rate is 4%. The current price of Ford stock is $50. Assume that no dividends are paid on the Ford stock over the next nine months.

(a) Find the values of u, d, r, and p for a three-period binomial that you may use to price a nine-month option.

(b) Using a three-period binomial model, find the price of a nine-month European put option on Ford with a strike price of 60.

(c) Using the same model (a three-period binomial model) find the price of a nine-month American put option on Ford with a strike price of 60.

(d) At the start of the tree (i.e. today) what are and L for the portfolio that replicates the American put option?

(e) Assuming that the stock price moves up over the first three months, determine how the composition of the replicating portfolio would change. That is, how many additional shares would you buy/sell and how much additional cash would you borrow/lend? What is the net cost of these two transactions?

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