problems on Options and Options valuation
(1) Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and expirations of 6 months. What would be the profit to an investor who buys the call for $4 in the following scenarios for stock prices in 6 months? What would be the profit in each situation to an investor who buys the put for $6?
Prevailing stock price Value of call at expiration Initial cost Profit
a. $40
b. $45
c. $50
d. $55
e. $60
Prevailing stock price Value of put at expiration Initial cost Profit
a. $40
b. $45
c. $50
d. $55
e. $60
(2) Use the figures showing the prices of various IBM options to compute the payoff and the profits for investments in each of the following February maturity options, assuming that the stock price on the maturity date is $105.
a. Call option, K = $100
b. Put option, K = $100
c. Call option, K = $105
d. Put option, K = $105
e. Call option, K = $110
f. Put option, K = $110
(3) The common stock of the PP Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out that range in the next 3 months. You don’t know whether it will go up or down, however. The present price of the stock is $100 per share, and the price of a 3-month call option at an exercise price of $100 is $10.
(a) If the risk-free interest rate is 10% per year, what should be the price of a 3-month put option on PP stock at an exercise price of $100? (The stock pays no dividends)
(b) What will be a simple options strategy to exploit your conviction about the stock price’s future movements? How far will it have to move in either direction for you to make a profit on your initial investment?
(4) The common stock of the CC Corporation has been trading in a narrow price range of around $50 for months, and you are convinced it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $50 is $4.
(a) If the risk-free interest rate is 10% per year, what should be the price of a 3-month call option on CC stock at an exercise price of $50 if it is in the money? (The stock pays no dividends)
(b) What will be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movements? What is the most money you could make on this position? How far can the stock price move in either direction before you lose money?
(5) The present stock price of International Wood is $69 and the stock does not pay dividends. The immediate risk free rate of return is 10%. The immediate standard deviation of International Wood’s stock is 25%. You wish to purchase a call option on this stock with an exercise price of $70 and expiration date 73 days from now. Using the Black-Scholes Options Pricing Model, how much should the call option be worth today?
(6) The present stock price of International Wood is $69 and the stock does not pay dividends. The immediate risk free rate of return is 10%. The immediate standard deviation of International Wood’s stock is 25%. You wish to purchase a put option on this stock with an exercise price of $70 and expiration date 73 days from now. Using the Black-Scholes Options Pricing Model, how much should the put option be worth today?
PLEASE NOTE: SHOW ALL YOUR CALCULATIONS STEP IN STEP, AND CLEAR.