### Black-scholes options pricing model

Assignment Help Project Management
##### Reference no: EM13674

Questions 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 will be the profit to an investor who buys the call for \$4 in the following scenarios for stock prices in 6 months? What will be the profit in each scenario 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 attached showing the prices of various IBM options to calculate 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 do not know whether it will go up or down, however. The current 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 must be the price of a 3-month put option on PP stock at an exercise price of \$100?

(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?

(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 must be the price of a 3-month call option on CC stock at an exercise price of \$50 if it is in the money?

(b) What would 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 can make on this position? How far can the stock price move in either direction before you lose money?

(5) The current stock price of International Wood is \$69 and the stock does not pay dividends. The instantaneous risk free rate of return is 10%. The instantaneous 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 current stock price of International Wood is \$69 and the stock does not pay dividends. The instantaneous risk free rate of return is 10%. The instantaneous 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?

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