20. The common stock of the P.U.T.T. Corporation has been trading in a narrow pr
ID: 2794449 • Letter: 2
Question
20. The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month and you are convinced it is going to break far out of that range in the next 3 months. You do not know whether it will go up or down, however. The current price of the stock is $125 per share, and the price of a 3-month call option at an exercise price of $125 is $10.25. a. If the risk-free interest rate is 5% per year, what must be the price of a 3-month put option on PUTT. stock at an exercise price of $125? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Put-call parity b. What would be a simple options strategy to exploit your conviction about the stock price's future movements? How far would it have to move in either direction for you to make a profit on your initial investment? (Round your intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.) Total cost of the straddleExplanation / Answer
a. Call-put parity equation can be used to calculate put price in following manner
C + K* e^ (-r*t) = P + S0
Where,
C = Call premium =$10.25
K = exercise price of the call/put option =$125
P = Put premium =?
S0 = Current price of underlying stock =$125
e^ (-r*t) = the present value of the exercise price discounted from the expiration date at risk-free rate
And r =Risk-free rate per annum = 5% and t= time period =0.25 years (3 months)
Therefore,
New call-put parity equation
$10.25 + $125 *e^ (-5%*0.25) = P + $125
$10.25 + $123.45 = P + $125
Or P = $10.25 + $123.45 - $125 = $8.70
Price of put option should be $8.70
b. A straddle strategy can be used to exploit the market condition in any direction where one call option and one put option of a stock with same strike price and same expiry date are purchased.
The straddle will make the profit either at above the stock price = strike price + (Put price + call price)
Or at below the stock price = strike price - (Put price + call price)
And,
Total cost of straddle = Call price +Put price
= $10.25 + $8.70 = $18.95
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.