金融工程 第二次习题
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金融工程 第二次习题
1. An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield over
the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum and the
dividend yield over the next six months is 1% per annum. Estimate the futures price of the index
for three-month and six-month contracts. All interest rates and dividend yields are continuously
compounded.
2. Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per
annum and to receive 3-month LIBOR in return on a notional principal of $100 million with
payments being exchanged every 3 months. The swap has a remaining life of 14 months. The
average of the bid and offer fixed rates currently being swapped for 3-month LIBOR is 12% per
annum for all maturities. The 3-month LIBOR rate 1 month ago was 11.8% per annum. All rates
are compounded quarterly. What is the value of the swap?
3. Company A, a British manufacturer, wishes to borrow US dollars at a fixed rate of interest.
Company B, a US multinational, wishes to borrow sterling at a fixed rate of interest. They have
been quoted the following rates per annum (adjusted for differential tax effects):
Sterling US dollars
Company A 11.0% 7.0%
Company B 10.6%
6.2%
Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and
that will produce a gain of 15 basis points per annum for each of the two companies.
4. Suppose that1c,2c, and3care the prices of European call options with strike prices1K,2K,
and3K, respectively, where3K>2K>1Kand1223KKKK. All options have the same
maturity. Show that
5. 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
6. 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?
7. Calculate the intrinsic value and time value from the mid-market (average of bid and offer)
prices the September 2013 call options in Table 1.2. Do the same for the September 2013 put
options in Table 1.3. Assume in each case that the current mid-market stock price is $871.30.
8. The price of a European call that expires in six months and has a strike price of $30 is $2. The
underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five
months. Interest rates (all maturities) are 10%. What is the price of a European put option that expires in six months and has a strike price of $30?
9. 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.
