Question

Consider the following options on Goldman Sachs’ stock with current price of $120. Assume you have enough money in your brokerage account to cover the margin required to write calls and puts.

Type Exercise price Option premium per share

Call $115 $9.20

Put $120 $4.50

Call $125 $3.70

a) How much is required (or received) UP FRONT if you buy 100 shares of calls with $115 exercise price, sell 200 shares of puts with $120 exercise price, and sell 100 shares of calls with $125 exercise price? b) What would be your net profit or loss for your portfolio in (a) if the stock price is $118 at maturity date?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L
2
3		Type	Exercise Price	Option premium per share
4		Call	115	9.2
5		Put	120	4.5
6		Call	125	3.7
7
8
9		a)
10
11		Type	Exercise Price	Option premium per share	Buy or Sell	Quantity	Amount Received (Required)
12		Call	115	9.2	Buy	100	=-E12*G12	=-E12*G12
13		Put	120	4.5	Sell	200	=E13*G13
14		Call	125	3.7	Sell	100	=E14*G14
15						Total	=SUM(H12:H14)
16
17		Hence amount received to buy the required quantity of call and put option	=H15
18
19		b)
20
21		Calculation of total profit:
22
23		For put option buyer, gain occurs when asset price falls.
24		Put option gives option buyer the right to sell the Stock at a strike price.
25
26		Profit of put option buyer is given by following equation:
27		Profit of put option = Max(X-ST,0)-p
28		where ST is stock price at maturity, X is exercise price and p is premium paid to buy the put option.
29
30		Call option gives option buyer the right to buy the Stock at a strike price at a specified time in future.
31
32		Profit of Call option buyer is given by following equation:
33		Profit of Call option = Max(ST-X,0) -c
34		where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.
35
36		Profit of Call option seller is given by following equation:
37		Profit of Call option seller = -(Max(ST-X,0) -c)
38		where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.
39
40		Price at the maturity	118
41
42		Type	Exercise Price	Option premium per share	Buy or Sell	Quantity	Profit (Loss)
43		Call	115	9.2	Buy	100	=G43*(MAX($D$40-D43,0)-E43)	=G43*(MAX($D$40-D43,0)-E43)
44		Put	120	4.5	Sell	200	=G44*-(MAX(D44-D40,0)-E44)	=G44*-(MAX(D44-D40,0)-E44)
45		Call	125	3.7	Sell	100	=G45*-(MAX($D$40-D45,0)-E45)	=G45*-(MAX($D$40-D45,0)-E45)
46						Total	=SUM(H43:H45)	=SUM(H43:H45)
47