Pay 5.0% Libor+60bps
Pay in Swap Libor 5.4%
Receive (5.3%) (Libor)
NET: Libor – 30 bps 6.0%
If no swap, ABC would have had to pay Libor + 10bps to get a floating rate loan, but instead pays Libor – 30 bps (a savings of 40 bps). XYZ would have had to pay 6.4% for a fixed rate loan, but instead pays 6%. The 10 bps difference goes to the intermediary and is funded entirely by XYZ Corp which is the low quality borrower.
- Explain carefully the difference between writing a put and buying a call option. Why are they grouped together when considering position limits?
Writing a put involves taking a short position in a put (you must buy back the stock at a higher price if the put is exercised), while long calls represent buying a call. Writers of puts have an obligation should the long put exercise the option, while call buyers have no obligation. Call buyers must pay a premium for the option. Short puts and long calls are both designed to profit in a bullish market. Thus, they are considered to be on the same side of the market.
- Explain the difference between an American option and a European option. What do they have in common?
An American option can be exercised at any time up to and including the expiration date. A European option can be exercised only on the expiration date. An American option is more valuable than a European option because it has all the features of a European option, plus early exercise.
4. Determine whether each of the following arrangements is an option. If so, decide whether it is a call or a put and identify the premium.
- You purchase automobile insurance for your car.
Auto insurance is a put option. In the event of loss, the insurance company pays you a portion of the value of your car. The premium on the put is insurance premium.
- You are a college senior evaluating possible job choices. One job promises that if you accept, it will guarantee your bonus for the next three years.
The guaranteed bonus is a call option granted to you by your employer. If you accept the job, you can “purchase” the bonus by accepting the job. The premium is that you have to take this job; of course, you do not have to exercise the option by continuing to stay at the job.
- You enter into a noncancelable, long-term apartment lease.
This is not an option since no one has the opportunity to forego exercise. It is actually a forward contract. If the lease were cancelable over the period during which the rental rate was fixed, it would be a call option.
5. What is the lower bound for the price of a four-month call option on a non-dividend paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% p.a.?
The lower bound is 28-25e-0.08*0.3333 = $3.66
6. A 4-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in one-month. The risk-free interest rate is 12% p.a. for all maturities. What opportunities are there for an arbitrageur?
The present value of the strike price is 60e-0.3333*0.12 = $57.65. The present value of the dividend is 0.80e-0.083333*0.12 = $0.79. Since $5 < $64-57.65-0.79, the no-arbitrage condition is violated. An arbitrageur should buy the option and short the stock. Regardless of what happens a profit will materialize. If the stock price < 60, the arb loses $5 spent on the option, but gains at least $5.56 in present value terms from the short position. If the stock price > 60 at expiration, the arb gains exactly 5.56-5 = 0.56.
