Question

DEF stock currently trades at $112. Use the chart for the 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

1. 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.

2. 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.

a. true

b. false

3. 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.

$350

4. 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.

$2,025

I've bolded the answers I got and I would just like to check my work. Thank you!

Answer 1

1. As per the table, the exercise value of $115 Feb Put Option is 3.62

2. Synthetic 110 Jan Put Option = Buy Stock and Sell Call Option

Synthetic 110 Jan Put Option = 112 + 6.25

Premium for buying 110 Jan Put Option = -0.65

Payoff From Startegy = 112 +6.25-0.65 = 117.6

After 6 months, price of stock = 112*e^(0.05*6/12) = 114.83

Since Buying and selling a put therefore profit from strategy

= 117.6 - 114.83 = $2.77

So, it shows there is arbitrage opportunity.

Answer is True

3. For Short Strip Position - Sell One Call option and two Put Option

Stock Price at Expiry = $110

Profit From One Call Jan 105 = (7.5)-(110-105) = 2.5

Profit From Two Put Jan 105 = 0.50*2 - 0 = 1

Profit From Long Strap Position = 1+2.5= $3.5

4. For Long strap Position - Buy One Put option and two Call Option

Stock Price at Expiry =$127

Profit From One Put Feb 110 =  -0.75*2 = -1.5

Profit From Two Call Feb 110 = 2*(127-110)-(6.5*2) = 21

Profit From Long Strap Position = 21-1.5 = $19.5