Question 2 (40%) (A) Use the data below. Assume 365 days in a year. Stock price today 5.03 Exercise price 5.00 Maturity 156 days Standard deviation of stock return 65% per year Risk-free interest rate 1% per year i. Calculate the option value if it is a European call option. ii. Calculate the option value if it is a European put option. (B) If the options in (A) above were American options, would the answer in (A)-i and (A)-ii have changed? Explain. No calculation needed. (C) Use a one-period binomial tree and find the value of the European put option in (A)-ii. (D) Replicate an investment in the stock in (C) by a combination of put options and risk-free lending. (E) Fill in the table below. Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST E 35 Profit/loss at ST = 47 (1) long a stock (S=45) (2) long one put (EX=45, p=6) Combination of (1) + (2) Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST = 35 Profit/loss at ST = 47 (3) long one call (EX= 45, c=3) (4) write one call (Ex= 40, C=5) Combination of (3) + (4) Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST = 35 Profit/loss at ST = 47 (5) write one call (EX=45, C=3) (6) write one put (EX= 45, p=6) Combination of (5) + (6) Question 2 (40%) (A) Use the data below. Assume 365 days in a year. Stock price today 5.03 Exercise price 5.00 Maturity 156 days Standard deviation of stock return 65% per year Risk-free interest rate 1% per year i. Calculate the option value if it is a European call option. ii. Calculate the option value if it is a European put option. (B) If the options in (A) above were American options, would the answer in (A)-i and (A)-ii have changed? Explain. No calculation needed. (C) Use a one-period binomial tree and find the value of the European put option in (A)-ii. (D) Replicate an investment in the stock in (C) by a combination of put options and risk-free lending. (E) Fill in the table below. Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST E 35 Profit/loss at ST = 47 (1) long a stock (S=45) (2) long one put (EX=45, p=6) Combination of (1) + (2) Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST = 35 Profit/loss at ST = 47 (3) long one call (EX= 45, c=3) (4) write one call (Ex= 40, C=5) Combination of (3) + (4) Maximum Maximum Break-even profit(s) loss(es) price(s) Profit/loss at ST = 35 Profit/loss at ST = 47 (5) write one call (EX=45, C=3) (6) write one put (EX= 45, p=6) Combination of (5) + (6)
