Question

3. We short one share of a non-dividend paying stock for S(0) = $98. We insure this postion with a 1-year 96-strike call whose premium is $7.90. (1) What is the maximum loss on this position? (2) What is the break even point? (3) Draw and label a profit diagram for this position. (4) What is the maximum profit for this position? 4. Suppose a 1-year put on index S costs $3.315 and a 1-year call, of the same strike, costs $5.530. What is the strike of the put and call if the 1-year forward price is $100, and the continuous interest rate is 2%?

Answer 1

Short one share of a non-dividend paying stock fro S(0) = 98$

Insure this position with a 1 year 96 -strike call whose premium = 7.90$

1. Ans : maximum loss on this position is

At short is unlimited and at call option is premium only but short is cover by call option so by combination of both max. loss is net payoff =

{(short price -spot price of stock)+                                                             for short position payoff

Only positive value(spot price of stock – strike price) or take 0 }        for option

• Cost of premium

Price of stock	98 price short postion pay off	premium 7.90 payoff	total payoff	cost of premium	net payoff
90	8	0	8	7.9	0.1
91	7	0	7	7.9	-0.9
92	6	0	6	7.9	-1.9
93	5	0	5	7.9	-2.9
94	4	0	4	7.9	-3.9
95	3	0	3	7.9	-4.9
96	2	0	2	7.9	-5.9
97	1	1	2	7.9	-5.9
98	0	2	2	7.9	-5.9
99	-1	3	2	7.9	-5.9
100	-2	4	2	7.9	-5.9
101	-3	5	2	7.9	-5.9
102	-4	6	2	7.9	-5.9
103	-5	7	2	7.9	-5.9
104	-6	8	2	7.9	-5.9
105	-7	9	2	7.9	-5.9
106	-8	10	2	7.9	-5.9
107	-9	11	2	7.9	-5.9
108	-10	12	2	7.9	-5.9
109	-11	13	2	7.9	-5.9
110	-12	14	2	7.9	-5.9

So as per illustration maximum loss is 5.90$ is possible

2. Ans : Break even point of this strategy is net pay off is 0 so

Net payoff =

{(short price -spot price of stock(X))+                                                             for short position payoff

Only positive value(spot price of stock(X) – strike price) or take 0 }        for option

-Cost of premium(7.90)

0 ={(98-X) + (X-96)}-7.90     it can’t be solve by take this equation so, put 2 condition  

Case I option payoff is 0 then

0 = {98-X +0} – 7.90    = 90.10-X       so              X   =   90.10        Ans

Case ll short payoff is 0 then it is possible only if stock price is 98 at spot but at this condition payoff is not 0 so that is not break even point.

3. Ans : Payoff diagram as per table above for this strategy :

Profit Loss معده با حبیب یہ حر جرایم این اذان و ادامه 80 95اوو 85 100 105

4. Ans : maximum profit is unlimited as per diagram and strategy but stock minimum price is possible is 0 their for maximum profit calculate take stock price 0 as spot at this call payoff also is o so net payoff

= {(98-0)+0)}-7.90    = 98-7.90   = 90.10$ Ans.