Please Solve the all the problems given below on Mechanics of Options Markets
Practice Questions
Problem 1.
A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter market for trading?
Problem 2.
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.
Problem 3.
Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.
Problem 4.
Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that the European put option has the same value as a European call option with the same strike price and maturity.
Problem 5.
A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the variation of the trader's profit with the asset price.
Problem 6.
Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.
Problem 7.
Explain why an American option is always worth at least as much as its intrinsic value.
Problem 8.
Explain carefully the difference between writing a put option and buying a call option.
Problem 9.
The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each.
Problem 10.
Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months. Explain how the terms of the option contract change when there is
a) A 10% stock dividend
b) A 10% cash dividend
c) A 4-for-1 stock split
Problem 11.
"If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months." Discuss this statement.
Problem 12.
What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?
Problem 13.
Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?
Problem 14.
Explain why the market maker's bid-offer spread represents a real cost to options investors.
Problem 15.
A United States investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
Further Questions
Problem 16.
Calculate the intrinsic value and time value from the mid-market (average of bid and offer) prices the July 2012 call options in Table 1.2. Do the same for the July 2012 put options in Table 1.3. Assume in each case that the current mid-market stock price is $561.40.
Problem 17
A trader has a put option contract to sell 100 shares of a stock for a strike price of $60.
What is the effect on the terms of the contract of:
Problem 18
A trader writes five naked put option contracts, with each contract being on 100 shares.
The option price is $10, the time to maturity is six months, and the strike price is $64.
(a) What is the margin requirement if the stock price is $58?
(b) How would the answer to (a) change if the rules for index options applied?
(c) How would the answer to (a) change if the stock price were $70?
(d) How would the answer to (a) change if the trader is buying instead of selling the Options?
Problem 19.
The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor's profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?
Problem 20.
"If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense" Discuss this viewpoint. Can you think of alternatives to the usual executive stock option plan that take the viewpoint into account?
Problem 21.
Use DerivaGem to calculate the value of an American put option on a nondividend paying stock when the stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 1.5 years. (Choose binomial American for the "option type" and 50 time steps.)
Problem 22.
On July 20, 2004 Microsoft surprised the market by announcing a $3 dividend. The ex-dividend date was November 17, 2004 and the payment date was December 2, 2004. Its stock price at the time was about $28. It also changed the terms of its employee stock options so that each exercise price was adjusted downward to
Pre-dividend Exercise Price
The number of shares covered by each stock option outstanding was adjusted upward to Number of Shares Pre-dividend "Closing Price" means the official NASDAQ closing price of a share of Microsoft common stock on the last trading day before the ex-dividend date.
Evaluate this adjustment. Compare it with the system used by exchanges to adjust for extraordinary dividends