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Dæmi fyrir dæmatíma 2:

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5.12:
A financial institution has entered into an interest rate swap with company X.  Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years.  Payments are made every six months.  Suppose that company X defaults on the sixth payment date (end of year 3) when the interest rate (with semiannual compounding) is 8% per annum for all maturities.  What is the loss to the financial institution?  Assume that six-month LIBOR was 9% per annum halfway through year 3.

6.5:
Explain carefully the difference between writing a call option and buying a put option.

6.8:
"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.

6.12:
An 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?

6.13:
An investor buys 500 shares of stock and sells five call option contracts on the stock.  The strike price is $30.  The price of the option is $3.  What is the investor's minimum cash investment (a) if the stock price is $28 and (b) if the stock price is $32?

7.7:
Give two reasons why the early exercise of an American call option on a non-dividend-paying stock is not optimal.  The first reason should involve the time value of money.  The second reason should apply even if interest rates are zero.

7.8:
"The early exercise of an American put is a trade off between the time value of money and the insurance value of a put."  Explain this statement.

7.9:
A European call and put option on a stock both have a strike price of $20 and an expiration date in three months.  Both sell for $3.  The risk-free interest rate is 10% per annum, the current stock price is $19, and a $1 dividend is expected in one month.  Identify the arbitrage opportunity open to a trader.

7.13:
A four-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% per annum for all maturities.  What opportunities are there for an arbitrageur?

7.18:
The price of an American call on a non-dividend-paying stock is $4.  The stock price is $31, the strike price is $30, and the expiration date is in three months.  The risk-free interest rate is 8%.  Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.