Question

1. For the following options on Dec 18 corn futures, calculate the breakeven point and draw the pay-off diagram.

a) Writing a put with a $4.00 strike price and a premium of $0.27

b) Holding a put with a $4.00 strike price and a premium of $0.27

c) Writing a call with a $4.10 strike price and a premium of $0.18

d) Holding a call with a $4.10 strike price and a premium of $0.18

Answer 1

S = Stock price at expiration, K = strike price, C = Call premium, P = Put premium

Net gain / (loss) from writing a put option = P - max (K - S, 0)

Net gain / (loss) from holding a put option = max (K - S, 0) - P

Net gain / (loss) from writing a call option = C - max (S - K, 0)

Net gain / (loss) from holding a call option = max (S - K, 0) - C

a) Writing a put with a $4.00 strike price and a premium of $0.27

Net gain / (loss) from writing the put option = P - max (K - S, 0) = 0.27 - max (4 - S, 0)

Break even point: 0.27 - max (4 - S, 0) = 0; hence 0.27 - (4 - S) = 0; hence, S = 4 - 0.27 = 3.73

The gain / (loss) matrix is as shown below:

S	Gain / (Loss)
	0.27 - max (4 - S, 0)
1.00	-2.73
2.00	-1.73
3.00	-0.73
3.73	0
5.00	0.27
6.00	0.27
7.00	0.27
8.00	0.27

And the payoff diagram is as shown below

b) Holding a put with a $4.00 strike price and a premium of $0.27

Net gain / (loss) from holding the put option = max (K - S, 0) - P = max (4 - S, 0) - 0.27

Break even point: max (4 - S, 0) - 0.27 = 0

Or, 4 - S - 0.27 = 0

Or, S = 4 - 0.27 = 3.23

Gain / (Loss) matrix:

S	Gain / (Loss)
	max (4 - S, 0) - 0.27
1.00	2.73
2.00	1.73
3.00	0.73
3.73	-
5.00	(0.27)
6.00	(0.27)
7.00	(0.27)
8.00	(0.27)

And the gain / (loss) diagram is:

c) Writing a call with a $4.10 strike price and a premium of $0.18

Net gain / (loss) from writing a call option = C - max (S - K, 0) = 0.18 - max (S - 4.10, 0)

Break even point: 0.18 - max (S - 4.10, 0) = 0.18 - (S - 4.10) = 4.28 - S = 0; hence, S = 4.28

Gain / (Loss) matrix is:

S	Gain / (Loss)
	0.18 - max (S - 4.10, 0)
1.00	0.18
2.00	0.18
3.00	0.18
4.00	0.18
4.28	(0.00)
6.00	(1.72)
7.00	(2.72)
8.00	(3.72)

And the gain / (loss) diagram is:

d) Holding a call with a $4.10 strike price and a premium of $0.18

Net gain / (loss) from holding a call option = max (S - K, 0) - C = max (S - 4.10, 0) - 0.18

Break even point: max (S - 4.10, 0) - 0.18 = S - 4.10 - 0.18 = 0; hence, S = 4.28

Gain / (Loss) matrix is:

S	Gain / (Loss)
	max (S - 4.10, 0)- 0.18
1.00	(0.18)
2.00	(0.18)
3.00	(0.18)
4.00	(0.18)
4.28	0.00
6.00	1.72
7.00	2.72
8.00	3.72

And the gain / (loss) diagram is: