1) A five-year interest rate swap that can be canceled at the two year point is (Circle
one)
a. The difference between two plain vanilla interest rate swaps
b. The difference between a a plain vanilla interest rate swap and a forward start swap
c. A regular interest rate swap plus a European swap option
d. A regular interest rate swap plus a Bermudan swap option
2) As the barrier is observed more frequently, a knock out option becomes (Circle one)
a. More valuable
b. Less valuable
c. There is no effect on value
d. May become more valuable or less valuable
3) When there are two dividends on a stock, Blacks approximation sets the value of an
American call option equal to (circle one)
a. The value of a European option maturing just before the first dividend
b. The value of a European option maturing just before the second dividend
c. The greater of the values in (a) and (b)
d. None of the above
4) Suppose you enter into an interest rate swap where you are receiving floating and
paying fixed. Which two of the following is true? (circle two)
a. Your credit risk is greater when the term structure is upward sloping than when it is
downward sloping
b. Your credit risk is greater when the term structure is downward sloping than when it
is upward sloping
c. Your credit risk exposure increases when interest rates decline unexpectedly
d. Your credit risk exposure increases when interest rates increase unexpectedly
5) Consider an exchange traded put option to sell 100 shares for $20. Give (a) the strike
price and (b) the number of shares that can be sold after
i. A 5 for 1 stock split
ii. A 25% stock dividend
iii. A $5 cash dividend
6) Which of the following lead to IBM issuing more shares (circle three)
a. Some executive stock options are exercised
b. Some exchange-traded put options are exercised
c. Some exchange-traded call options are exercised
d. Some warrants on IBM are exercised
e. Some of IBMs convertible debt is converted to equity
7) The yield on a companys five-year bonds is 5%. The five year swap rate is 4% and
the five-year Treasury rate is 4.5%. You would expect the five-year CDS spread to be
approximately (Circle one)
a. 200 basis points
b. 150 basis points
c. 100 basis points
d. 50 basis points
8) A put option on the S&P 500 has an exercise price of 500 and a time to maturity of
one year. The risk free rate is 7% and the dividend yield on the index is 3%. The
volatility of the index is 20% per annum and the current level of the index is 500 . A
financial institution has a short position in the option.
a) Calculate the delta, gamma, and vega of the position. Explain how they can be
interpreted.
b) How can the position be made delta neutral?
c) Suppose that one week later the index has increased to 515. How can delta neutrality
be preserved?
9) Vega measures (circle one)
a. The rate of change of delta with the asset price
b. The rate of change of the portfolio value with the passage of time
c. The sensitivity of the portfolio value to interest rate changes
d. None of the above
10) Which of following is applicable to corporate bonds in the United States (circle
one)
a. Actual/360
b. Actual/Actual
c. 30/360
d. Actual/365
11) The spot price of an asset is positively correlated with the market. Which of the
following would you expect to be true (circle one)
a. The forward price equals the expected future spot price
b. The forward price is greater than the expected future spot price
c. The forward price is less than the expected future spot price
d. The forward price is sometimes greater and sometimes less than the expected future
spot price
12) To create a range forward contract in order to hedge foreign currency that will be
paid a company should (Circle one)
a. Buy a put and sell a call on the currency with the strike price of the put higher than
that of the call
b. Buy a put and sell a call on the currency with the strike price of the put lower than
that of the call
c. Buy a call and sell a put on the currency with the strike price of the put higher than
that of the call
d. Buy a call and sell a put on the currency with the strike price of the put lower than
that of the call
13) Futures contracts trade with every month as a delivery month. A company is
hedging the purchase of the underlying asset on June 15 . Which futures contract should
it use (circle one)
a. The June contract
b. The July contract
c. The May contract
d. The August contract
14) A PO is a principal only MBS and an IO is an interest only MBS. As prepayments
increase the following happens (Circle one)
a. Both the PO and IO become more valuable
b. The PO becomes more valuable and the IO becomes less valuable\
c. The PO becomes less valuable and the IO becomes more valuable
d. Both the PO and IO become less valuable
15) Is it ever optimal to exercise early an American call option on a) the spot price of
gold, b) the spot price of copper, c) the futures price of gold, and d) the average price of
gold measured between time zero and the current time. Explain your answers.
16) A box spread is a combination of a bull spread composed of two call options with
strike prices and and a bear spread composed of two put options with the same
two strike prices.
a. Describe the payoff from a box spread on the expiration date of the options.
b. What would be a fair price for the box spread today? Define variables as necessary.
c. Under what circumstances might an investor choose to construct a box spread?
d. What sort of investor do you think is most likely to invest in such an option
combination, i.e. a hedger, speculator or arbitrageur? Explain your answer.
17) Which of the following is true about employee stock options (ESOPS) and regular
American exchange-traded call options (EXOPS). (Circle three)
a. ESOPS usually cannot be exercised at all times whereas EXOPS can
b. ESOPS cannot be traded
c. The exercise of EXOPS affects the number of shares outstanding
d. ESOPS can be exercised only at maturity whereas EXOPS can usually be exercised
prior to maturity
e. Employees are usually liable to forfeit their ESOPS if they leave the company
f. Shareholders suffer dilution at the time ESOPS are exercised
18) Which of the following is true? Circle one.
a. Both forward and futures contracts are traded on exchanges
b. Forward contracts are traded on exchanges, but futures contracts are not
c. Futures contracts are traded on exchanges, but forward contracts are not
d. Neither futures contracts nor forward contracts are traded on exchanges
19) . It is May 1 . The quoted price of a bond with a 30/360 day count and 12% per
annum coupon in the United States is 105 . It has a face value of 100 and pays coupons
on April 1 and October 1 . What, to two decimal place accuracy, is the cash price?
20) Suppose that the yield curve is flat at 5% per annum with continuous compounding.
A swap with a notional principal of $100 million in which 6% is received and
six-month LIBOR is paid will last another 15 months. Payments are exchanged every
six months. The six-month LIBOR rate at the last reset date (three months ago) was 7%.
Answer in millions of dollars to two decimal places.
i. What is the value of the fixed-rate bond underlying the swap?
ii. What is the value of the floating-rate bond underlying the swap?
iii. What is the value of the payment that will be exchanged in 3 months?
iv. What is the value of the payment that will be exchanged in 9 months?
v. What is the value of the payment that will be exchanged in 15 months?
vi. What is the value of the swap?
21) A portfolio is worth $24,000,000. The futures price for a Treasury note futures
contract is 110 and each contract is for the delivery of bonds with a face value of
$100,000. On the delivery date the duration of the bond that is expected to be cheapest
to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many
contracts are necessary for hedging the portfolio?
22) A short forward contract that was negotiated some time ago will expire in three
months and has a delivery price of $40. The current forward price for three-month
forward contract is $42. The three month risk-free interest rate (with continuous
compounding) is 8%. What to the nearest cent is the value of the short forward
contract?
23) The six-month zero rate is 8% with semiannual compounding. The price of a
one-year bond that provides a coupon of 6% per annum semiannually is 97 . What is the
one-year continuously compounded zero rate? Answer as a percent with two decimal
place accuracy
24) The current price of a non-dividend-paying stock is $30. Over the next six months it
is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero
i. What long position in the stock is necessary to hedge a short call option when the
strike price is $32? Give the number of shares purchased as a percentage of the number
of options that have been sold
ii. What is the value the call option
iii. What long position in the stock is necessary to hedge a long put option when the
strike price is $32. Give the number of shares purchased as a percentage of the number
of options purchased option
iv. What is the value of the put option
v. What is the risk neutral probability of the stock price moving up