The common stock of Company XYZ is currently trading at a price of $42. Both a put and a call option are available for XYZ stock, each having an exercise price of $40 and an expiration date in exactly six months. The current market prices for the put and call are $1.45 and $3.90, respectively. The risk-free holding period return for the next six months is 4 percent, which corresponds to an 8 percent annual rate.
a. For each possible stock price in the following sequence, calculate the expiration date payoffs (net of the initial purchase price) for the following positions: (1) buy one XYZ call option, and (2) short one XYZ call option:
20, 25, 30, 35, 40, 45, 50, 55, 60
Draw a graph of these payoff relationships, using net profit on the vertical axis and potential expiration date stock price on the horizontal axis. Be sure to specify the prices at which these respective positions will break even (i.e., produce a net profit of zero).
b. Using the same potential stock prices as in Part a, calculate the expiration date payoffs and profits (net of the initial purchase price) for the following positions: (1) buy one XYZ put option, and (2) short one XYZ put option. Draw a graph of these relationships, labeling the prices at which these investments will break even.
c. Determine whether the $2.45 difference in the market prices between the call and put options is consistent with the put-call parity relationship for European-style contracts.