Question

Three different call options on the same stock with the same expiration date have the following strike prices and option prices:

Strike Price	Call Price
$90	$22.70
$100	$16.20
$110	$13.70

A. Construct a payoff table and draw a profit diagram for an option strategy where you buy 1 $90 call, buy 1 $110 call, and write 2 $100 calls.
B. Calculate the payoffs and profits assuming the spot price is $98 at expiry.
C. What is/are the breakeven price(s), maximum reward, and maximum risk?
D. Describe in what circumstances it might make sense to invest in this package?

Answer 1

a.)

Total investment for entering the strategy = -22.7-13.7+ 2*16.2 = -$4

Stock price at maturiy T	Payoff from $90 long call	Payoff from $110 long call	Payoff from two $100 short calls	Net profit/loss
85	-22.7	-13.7	32.4	-4
86	-22.7	-13.7	32.4	-4
87	-22.7	-13.7	32.4	-4
88	-22.7	-13.7	32.4	-4
89	-22.7	-13.7	32.4	-4
90	-22.7	-13.7	32.4	-4
91	-21.7	-13.7	32.4	-3
92	-20.7	-13.7	32.4	-2
93	-19.7	-13.7	32.4	-1
94	-18.7	-13.7	32.4	0
95	-17.7	-13.7	32.4	1
96	-16.7	-13.7	32.4	2
97	-15.7	-13.7	32.4	3
98	-14.7	-13.7	32.4	4
99	-13.7	-13.7	32.4	5
100	-12.7	-13.7	32.4	6
101	-11.7	-13.7	30.4	5
102	-10.7	-13.7	28.4	4
103	-9.7	-13.7	26.4	3
104	-8.7	-13.7	24.4	2
105	-7.7	-13.7	22.4	1
106	-6.7	-13.7	20.4	0
107	-5.7	-13.7	18.4	-1
108	-4.7	-13.7	16.4	-2
109	-3.7	-13.7	14.4	-3
110	-2.7	-13.7	12.4	-4
111	-1.7	-12.7	10.4	-4
112	-0.7	-11.7	8.4	-4
113	0.3	-10.7	6.4	-4
114	1.3	-9.7	4.4	-4
115	2.3	-8.7	2.4	-4
116	3.3	-7.7	0.4	-4
117	4.3	-6.7	-1.6	-4
118	5.3	-5.7	-3.6	-4
119	6.3	-4.7	-5.6	-4
120	7.3	-3.7	-7.6	-4

b)

Stock price at maturiy T	Payoff from $90 long call	Payoff from $110 long call	Payoff from two $100 short calls	Net profit/loss
98	-14.7	-13.7	32.4	4

Hence, if the spot price is $98 at maturity, profit is $4

c.) The breakeven price are $94 and $106 ie. as long as the stock price at maturity is between 94 and 106, the strategy is profitable

Maximum reward = $6

Maximum risk = $4

d.) It makes sense to invest in this package if the investor believes that the stock prices would remain close to $100 at maturity and speculates that there won't be any huge price movement from $100