Options on EMP Inc expire in one year. An investor enters into the following pos
ID: 2617080 • Letter: O
Question
Options on EMP Inc expire in one year. An investor enters into the following positions:
(i) Buy a call option with an exercise price of $100. The premium is $15.
(ii) Sell a put option with an exercise price of $100. The premium is $20.
a) (5 points) You believe that one year from now the price per share will be $125.00. Calculate your expected profit or loss, including the premium paid or received from each of the investments above.
b) (5 points) Find the current market price of this stock. Assume that the risk-free annual interest rate is 4%.
c) (5 points) Choose the diagram below that best represents the payoff diagram of a portfolio consisting of the above call and put and a zero-coupon bond maturing in one year with face value of $100. (The diagrams ignore the premia paid and received). Type an ‘X’ in the outlined and highlighted cell above the diagram you choose. There are 5 choices, labeled Diagram A through Diagram E (Scroll right to see all choices) Choose only one diagram, or the response will be counted as incorrect.
Diagram A Diagram B Diagram C DiagramD Diagram E Payo Diagram Choice A Payoff Diagram Choice B Payoff Diagram Choice C Payoff Diagram Choice D Payoff Diagram Choice E 100 100 100 200 100 100 100 200 100 100 Value of Underlying (EMP) Value of Underlying (EMP) Value of Underlying (EMP) Vallue of Underlying (EMP) Value of Underlying (EMP)Explanation / Answer
(a) in the first instance it's look like investor is bullish on the market.
profit on call option = $25 - $ 15= $10 ( $ 25 is profit where as $15 is premium paid)
profit on put option = $20 wich is premium received ( note 1)
total profit $30
note 1 as in the case of put option price of the stock is higher hence put holder will not exercise it's right to sell hence option will not be exercised
(b) price of the stock can be done by put call parity where price of call as well as put is given
= c + x.e-rt =p + so. where c = pprice of call , x= strick price , p =price of put and sp = current stock price
= 15 + 100/1.04= 20 + so
so = $ 91.15
(c) as per my opinion diagram A will be selected as it shown as gross pay off I.e profit before premium
hence if stock price is 100 then pay off will be 0 as our strike price is also 100
if stock price is 200 then our pay off will be 100 to buy call option
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