Question

3. Suppose that call options on a stock with strike prices $40 and $45 cost $5 and $4, respectively. They both have 10-month maturity. (a) How can those two call options be used to create a bull spread?

(b) What is the initial investment?

(c) Construct a table showing how payoff and profit varies with ST in 10 month, for the bull spread you created. The table should looks like this:

Stock Price	Payoff	Profit
ST < K1
K1 < ST < K2
ST ≥ K2

Answer 1

A	B	C	D	E	F	G	H	I
2
3		Option type	Strike price	Premium	Maturity
4		Call	$40	$5	10 month
5		Call	$45	$4	10 month
6
7		3)
8		a)
9		Bull call spread is created by taking long position on call option with lower strike price
10		and short position on call option with higher strike rate of same maturity.
11
12		Thus the bull call spread will be created by buying the call option with strike price
13		of $40 and selling call option with strike price of $45.
14		b)
15		Total Investment required	=Premium to buy $40 Call option - Premium Received from sell of $45 call option
16			=$5 - $4
17			$1	=E4-E5
18
19		Thus initial investment required is	$1
20
21		c)
22
23		Call option gives option buyer the right to buy the Stock at a strike price at a specified time in future.
24
25		Payoff of Call option buyer is given by following equation:
26		Payoff of Call option = Max(ST-X,0)
27		where ST is stock price at maturity and X is exercise price
28
29		Payoff of Call option seller is given by following equation:
30		Payoff of Call option seller = -Max(ST-X,0)
31		where ST is stock price at maturity and X is exercise price
32
33		Profit of Call option buyer is given by following equation:
34		Profit of Call option = Max(ST-X,0) -c
35		where ST is stock price at maturity, X is exercise price and c is the premium paid to buy the Call option.
36
37		Profit of Call option seller is given by following equation:
38		Profit of Call option seller = -(Max(ST-X,0) -c)
39		where ST is stock price at maturity, X is exercise price and c is the premium paid to buy the Call option.
40
41		Stock Price	Payoff	Profit
42		ST<K1	0	($1)
43
44		K1<ST<K2	=(ST-K1)-0	=ST-K1-5+4
45			=ST-K1	=ST-K1-1
46
47
48		ST>=K2	=(ST-K1)-(ST-K2)	=(ST-K1)-5-(ST-K2)+4
49			=K2-K1	=K2-K1-1
50
51
52		Hence,
53		Stock Price	Payoff	Profit
54		ST<K1	0	($1.00)
55		K1<ST<K2	=ST-40	=ST-41
56		ST>=K2	$5	$4
57