8.3.)An investor sells a European call option with strike price of K and maturity T and buys a put with the same strike price and maturity. Describe the investor's position. The payoff to the investor is
- max (ST - K , 0) + max(K - ST, 0)
This is K- ST in all circumstances. The investor's position is the same as a short position in a forward contract with delivery price K.
8 .4.)Explain why brokers require margins when clients write options but not when they buy options? When an investor buys an option, cash must be paid up front. There is no possibility of future liabilities and therefore no need for a margin account.. When an investor sells an option, there are potential future liabilities. To protect against the risk of a default, margins are required.
8.5.)A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b)May 30? On April 1 options trade with expiration months of April, May, August, and November. On May 30 options trade with expiration months of June, July, August, and November.
8.6.)A company declares a 2-for-l stock split. Explain how the terms change for a call option with a strike price of $60. The strike price is reduced to $30, and the option gives the holder the right to purchase twice as many shares.
8.7.)“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. The exercise of employee stock options usually leads to new shares being issued by the company and sold to the employee. This changes the amount of equity in the capital structure. When a regular exchange-traded option is exercised no new shares are issued and the company's capital structure is not affected.
8.8.)A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the Philadelphia Stock Exchange and (b the over the counter market for trading? The Philade1phia Exchange offers European and American options with standard strike prices and times to maturity. Options in the over-the-counter market have the advantage that they can be tailored to meet the precise needs of the treasurer. Their disadvantage is that they expose the treasurer to some credit risk. Exchanges organize their trading so that there is virtually no credit risk.
8.11.)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. The terminal value of the long forward contract is:
where ST is the price of the asset at maturity and Fo is the forward price of the asset at the time the portfolio is set up. (The delivery price in the forward contract is a1so Fo.) The termina1 va1ue of the put option is:
max (Fo - ST, 0)
The termina1 va1ue of the portfolio is therefore
ST - Fo + max(Fo - ST, 0)
=max(0 ， ST - Fo]
This is the same as the termina1 va1ue of a European call option with the same maturity as the forward contract and an exercise price equal to Fo. We have shown that the forward contract p1us the put is worth the same as a call with the same strike price and time to maturity as the put. The forward contract is worth zero at the time the portfo1io is set up. It follows that the put is worth the same as the call at the time the portfolio is set up.
8.13.)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. The ho1der of an American option has all the same rights as the ho1der...
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