Assignment 5 (Ch 10)

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Feb 20, 2024

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Assignment 5 (Chapter 10) 10.1. What is the difference between an American and a European option? American: Can be exercised any time until expiration date. European: Can only be exercised at expiration date. 10.2. What are the four types of option positions? Calls: Short & Long Puts: Short & Long 10.3. Give examples of three index options that trade on the CBOE? SPX: S&P 500 Index VIX: CBOE Volatility Index RUT: Russell 2000 Index 10.4. What is a flex option? Customizable option allowing parties to choose terms like strike price, expiration date, style of exercise. 10.5. Which of the following lead to adjustments to the terms of an exchange-traded option: (a) stock splits, (b) stock dividends, (c) cash dividends? Stock Splits, Stock Dividends 10.6. What is a position limit? What is its purpose? Restriction on the number of option contracts an investor can hold of the same security. This prevents speculation, market manipulation, and market stability purposes. 10.8. Explain why margin accounts are required when clients write options but not when they buy options. When writing options, there is an unlimited loss potential on either puts or calls. – Margin required. When buying options, maximum loss is limited to the premium paid. – No margin required. 10.9. A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30? a. April, May, August, November b. June, July, August, November 10.10. Explain carefully the difference between writing a put option and buying a call option.

Writing a put option: Sells the right for the option holder to an asset to the option writer at a specific price. Writer receives premium. Seller must buy if investor exercises. Buying a call option: Right to purchase an asset at a specific price. Pay premium. No obligation to buy. 10.11. An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option. Option exercised if stock price falls below $40 at maturity. Investor makes profit when price is $37 at maturity. 10.12. An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option. Option exercised if stock is above $50 at maturity. Investor makes profit when price is $54 at maturity. 10.14. A company declares a 2-for-1 stock split. Explain how the terms change for a call option with a strike price of $60. Strike price falls to $30 (60/2), shares double (from 100 to 200). 10.15. “Employee stock options issued by a company are different from regular exchange-traded call options on the company’s stock because they can affect the capital structure of the company.” Explain this statement. Employee stock options issued by a company can affect company structure by increasing the number of outstanding shares and/or dilute existing shareholders’ ownership. 10.17. 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. Seller makes profit if stock price at maturity is above $52. The option is exercised if stock falls below $60 at maturity.

10.19. 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. 10.20. 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. Because it provides more flexibility as it can be exercised any time up until its maturity date, European options can only be exercised at the maturity date. If profits are good, American options allow investors to take advantage of their early position. Or leave their position if lower profits are expected later in the future for loss mitigation. 10.21. Explain why an American option is always worth at least as much as its intrinsic value. Potential to limit upside/downside risk, early exercise, and potential arbitrage. If both are priced the same, with these additional variables American options will always be worth more. 10.23. Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in 4 months. Explain how the terms of the option contract change when there is: (a) a 10% stock dividend; (b) a 10% cash dividend; and (c) a 4-for-1 stock split.

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a. 10% increase in shares = 550 share contract b. No effect c. 500x4 = 2000 shares, each contract worth 40/4=$10 10.27. Explain why the market maker’s bid–ask spread represents a real cost to options investors. The market makers’ bid-ask spread represents a real cost to options investors as 10.30. A trader writes 5 naked put option contracts with each contract being on 100 shares. The option price is $10, the time to maturity is 6 months, and the strike price is $64. What is the margin requirement if the stock price is $58? Assuming 20% 500*(10+(0.2*58)) =10800 How would the answer to (a) change if the rules for index options applied? Depends on the index. How would the answer to (a) change if the stock price were $70? 500*(10+(0.2*70))=12000 How would the answer to (a) change if the trader is buying instead of selling the options? No margin required.