The stock of Golden Corp. is currently trading for $15 per share. It pays no dividends. In
Question:
The stock of Golden Corp. is currently trading for $15 per share. It pays no dividends. In one year, the stock price will either go up by 20% or go down by 20%. The one-year risk-free rate is 4% and will remain constant.
(a) Using the binomial pricing model, calculate the price of a one-year European put option with a strike price of $17. What is the replicating portfolio in this case?
(6 marks)
(b) Suppose that the beta of Golden stock is 1.2. Calculate the leverage ratio and the beta of the put option.
(4 marks)
(c) According to put-call parity, what is the price of a one-year European call option on Golden stock with a strike price of $17?
(4 marks)
(d) Explain why an American call option on a non-dividend-paying stock always has the same price as its European counterpart. (Hint: Think about whether it is optimal to exercise an American call early.)
(5 marks)
(e) Equity can be viewed as a call option on the firm’s assets, while debt holders are short a put
option on the firm’s assets. Based on these views, explain why the asset substitution problem
arises.
(5 marks)