ABC's stock price is currently $40 per share. An at-the-money call option (X = $40) on ABC stock currently sells for $3, and an at-the-money put option sells for $2. The options expire in 6 months, and the risk-free rate of interest is 3 percent per annum.

a. Ignoring time value of money considerations, what are the profits or losses at expiration on a long call position, and on a short call position, at each of the following stock prices? What is the breakeven price of ABC stock for both positions?

S_T Profit on Long Call Profit on Short Call

20

30

40

50

60

Breakeven S_T = ________

b. Ignoring time value of money considerations, what are the profits or losses at expiration on a long put position, and on a short put position, at each of the following stock prices? What is the breakeven price of ABC stock for both positions?

S_T Profit on Long Put Profit on Short Put

20

30

40

50

60

Breakeven S_T = ________

c. Now take time value of money into account. Based on the given prices for the call and put options, does put-call parity hold? If put-call parity does not hold, show the transactions you would engage in to earn an arbitrage profit, and demonstrate that you earn a profit regardless of the price of ABC stock at the expiration of the options. You may assume for simplicity that transactions costs are zero and that you can either borrow or lend at the risk-free rate.