Question

1. Suppose you have the following 4 option contracts that expire in exactly 1 year from today.

	Premium	Strike Price
Call 1	$9.89	$75
Call 2	$4.98	$85
Put 1	$3.41	$75
Put 2	$8.30	$85

You establish an option position combining the purchase of Call 1 and Put 2 and the simultaneous sale of Call 2 and Put 1.

1. What is the cost of establishing this position?

2. Complete the following table, calculating the payoffs of the 4 options, the net cost of the position, and the profit of the overall combination.

Stock Price	$65	$70	$75	$80	$85	$90	$95
Payoff Long Call 1
Payoff Short Call 2
Payoff Long Put 2
Payoff Short Put 1
Terminal Value
Net Premium Paid
Profit

3. What must be the risk-free rate of return given what you found in part (b)?

Answer 1

	Premium	Strike Price
Call 1	$9.89 = C1	$75 = K1
Call 2	$4.98 = C2	$85 = K2
Put 1	$3.41 = P1	$75 = K1
Put 2	$8.30 = P2	$85 = K2

You establish an option position combining the purchase of Call 1 and Put 2 and the simultaneous sale of Call 2 and Put 1.

1. What is the cost of establishing this position?

Cost of establishing the position = C1 + P2 - C2 - P1 = 9.89 + 8.30 - 4.98 - 3.41 = $ 9.80

2. The payoff will be

Payoff from long call = max (S - K, 0)

Payoff from long Put = Max (K - S, 0)

Payoff from short call = - max (S - K, 0)

Payoff from short put = - max (K - S, 0)

Stock Price	$65	$70	$75	$80	$85	$90	$95
Payoff Long Call 1	0	0	0	5	10	15	20
Payoff Short Call 2	0	0	0	0	0	-5	-10
Payoff Long Put 2	10	5	0	0	0	0	0
Payoff Short Put 1	-20	-15	-10	-5	0	0	0
Terminal Value	-10	-10	-10	0	10	10	10
Net Premium Paid	9.80	9.80	9.80	9.80	9.80	9.80	9.80
Profit	-19.80	-19.80	-19.80	-9.80	0.20	0.20	020

3. What must be the risk-free rate of return given what you found in part (b)?

Risk free rate, r should be such that Terminal value of 10 = 9.80 x (1 + r)

Or, r = 10 / 9.80 - 1 = 2.04%