Question

Use the following table that shows the options available on DEF stock (which currently trades at $112) to answer the next seven questions.

	Call Premiums		Put Premiums
Strike	Jan.	Feb.	Jan.	Feb.
105	7.50	7.75	.50	.60
110	6.25	6.50	.65	.75
115	1.15	1.20	3.25	3.62
120	.75	.95	8.10	8.85 Question 15 What is the exercise value of the 115 Feb. put option? Round intermediate steps to four decimals and your final answer to two decimals. Do not use currency symbols or words when entering your response. 5 points Question 16 Assuming that the annual risk-free rate is 5% and the time until expiration is 6 months, an investor could earn an arbitrage profit by shorting a synthetic 110 Jan. put option and buying a 110 Jan. put option in the marketplace. True False 5 points Question 17 Suppose that you decided to set up a short strip position using the Jan. 105 options. Find your profit/loss if the stock trades for $110 when the options expire. Round intermediate steps to four decimals and your final answer to two decimals. Do not use the dollar sign when entering your answer. 5 points Question 18 Suppose that you decided to set up a long strap position using the Feb. 110 options. Find your profit/loss if the stock trades for $127 when the options expire. Round intermediate steps to four decimals and your final answer to two decimals. Do not use the dollar sign when entering your answer. 5 points Question 19 A hedge fund manager believed that DEF stock would be relatively stable over her investment horizon and decided to use the Feb 120 options to create a straddle position based on her belief. If the stock trades for $127 when the options expire, what is her profit/loss? -90 90 280 -280 None of the above 5 points Question 20 Suppose that you decided to create a long strangle position using the 115 Feb call and the 110 Feb put when the stock price traded at $112. Find your profit/loss if the stock trades at $118 when the options expire. 105 -105 605 -605 None of the above

Answer 1

Q15) The exercise price is 115 and the Put premium 3.62

hence, the following scenarios is possible

Strike Price	DEF stock Price	Put Premium	Cashflow	Remarks
115	116	3.62	0	Put lapses
115	115	3.62	0	Put lapses
115	114	3.62	-2.62	Put excercised
115	111.38	3.62	0.00	Put excercised
115	110	3.62	1.38	Put excercised

Put is excercided if stock price falls below 115 and the break even is achieved at 111.38

below stock price 111.38 the Cashflow is positive

16) The put call parity equation is given by

Put + Stock = Call + X/(1+r)^t

Where X is the Strike Price of the Options, R is the risk free rate and T is the time to maturity

from the above formula Synthetic put can be formed using

Put = Call + X/(1+r)^t- Stock

therefore to create s synthetic put we need to by a Call option , Invest Rs X/(1+r)^t and Short sell the stock

now strike price is 110 so our portfolio for Synthetic put consists

A	Call for strike price 110 (Jan)	6.25
B	X/(1+r)^t	110/(1+5%)^0.5
C	Stock	112
	Portfolio (A+B-C)	1.59900802

therefore the value of Synthetic 110 Jan Put is 1.6

Value of Actual 110 Jan Put is 0.65

Actual put is undervalued than synthetic put , therefore by purchasing actual put and selling synthetic put

We can earn an arbitrage profit of 1.6-0.65= 0.95 per share

Hence True

Q 17) Short strip means writing more put than Call

Suppose we write two puts and 1 Call for 105 strike price

so our revenue = call 105 jan = 7.5 Put jan = 0.5

total revenue = 2*0.5 + 7.5 = 8.5

At stock price put option gets expired but call is excersied

so call payout is 110-105 =5

therefore net profit is 8.5-5 = 3.5