Chapter 6
1. Which of following is applicable to corporate bonds in the United States? 30/360
2. It is May 1. The quoted price of a bond with an Actual/Actual (in period) day count and 12%
per annum coupon (paid semiannually) in the United States is 105. It has a face value of 100
and pays coupons on April 1 and October 1. What is the cash price? 105.98
3. 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 is the cash price? $106
4. The most recent settlement bond futures price is 103.5. Which of the following four bonds is
cheapest to deliver? Quoted bond price = 131; conversion factor = 1.2500
5. Which of the following is NOT an option open to the party with a short position in the
Treasury bond futures contract? The interest rate used in the calculation of the conversion
factor
6. A trader enters into a long position in one Eurodollar futures contract. How much does the
trader gain when the futures price quote increases by 6 basis points? $150
7. The bonds that can be delivered in a Treasury bond futures contract are Assets that provide
a known cash income
8. An ultra T-bond futures contract is one where Bonds with maturities greater than 25 year
can be delivered
9. 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? 200
10. Which of the following is true? The futures rates calculated from a Eurodollar futures quote
are always greater than the corresponding forward rate
11. How much is a basis point? 0.01%
12. Which of the following day count conventions applies to a US Treasury bond? Actual/Actual
(in period)
13. What is the quoted discount rate on a money market instrument? The interest rate earned
as a percentage of the final face value of a bond
14. Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8%
per annum semiannually? The yield on the bond is 10% per annum with continuous
compounding. 1.88
15. Which of the following is NOT true about duration? The prices of two bonds with the same
duration change by the same percentage amount when interest rate moves up by 100 basis
points
16. The conversion factor for a bond is approximately The price it would have if all cash flows
were discounted at 6% per annum
17. The time-to-maturity of a Eurodollars future contract is 4 years and the time-to-maturity of
the rate underlying the futures contract is 4.25 years. The standard deviation of the change
in the short term interest rate, ï ³ = 0.011. What does the model in the text give as the
difference between the futures and the forward interest rate. 0.103%
18. A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six months. How
many contracts are required? 10
19. In the U.S. what is the longest maturity for 3-month Eurodollar futures contracts? 10 years
20. Duration matching immunizes a portfolio against Small parallel shifts in the yield curve
Chapter 7
1. A company can invest funds for five years at LIBOR minus 30 basis points. The five-year swap
rate is 3%. What fixed rate of interest can the company earn by using the swap? 2.7%
2. Which of the following is true? The principal amounts usually flow in the opposite direction
to interest payments at the beginning of a currency swap and in the same direction as
interest payments at the end of the swap.
3. Company X and Company Y have been offered the following rates
4.
5.
6.
7.
8.
Fixed Rate
Floating Rate
Company X
3.5%
3-month LIBOR plus 10bp
Company Y
4.5%
3-month LIBOR plus 30 bp
Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a
swap with each other where the apparent benefits are shared equally, what is company X’s
effective borrowing rate? 3-month LIBOR -30bp
Which of the following describes the five-year swap rate? The average of A and B. (The fixed
rate of interest which a swap market maker is prepared to pay in exchange for LIBOR on a 5year swap & The fixed rate of interest which a swap market maker is prepared to receive in
exchange for LIBOR on a 5-year swap)
Which of the following is a use of a currency swap? All of the above. (To exchange an
investment in one currency for an investment in another currency. To take advantage
situations where the tax rates in two countries are different. To exchange borrowing in one
currency for borrowings in another currency)
The reference entity in a credit default swap is The company or country whose default is
being insured against
Which of the following describes an interest rate swap? All of the above (An agreement to
exchange interest at a fixed rate for interest at a floating rate, The exchange of a fixed rate
bond for a floating rate bond, A portfolio of forward rate agreements)
Which of the following is true for an interest rate swap? A swap is usually worth close to
zero when it is first negotiated
9. Which of the following is true for the party paying fixed in a newly negotiated interest
rate swap when the yield curve is upward sloping? The early forward contracts
underlying the swap have a negative value and the later ones have a positive value
10. A bank enters into a 3-year swap with company X where it pays LIBOR and receives 3.00%. It
enters into an offsetting swap with company Y where is receives LIBOR and pays 2.95%.
Which of the following is true: If company X defaults, the swap with company Y continues
11. When LIBOR is used as the discount rate: The floating rate bond underlying a swap is worth
par immediately after a pmnt date
12. A company enters into an interest rate swap where it is paying fixed and receiving LIBOR.
When interest rates increase, which of the following is true? The value of the swap to the
company increases
13. A floating for floating currency swap is equivalent to A fixed-for-fixed currency swap and two
interest rate swaps, one in each currency
14. A floating-for-fixed currency swap is equivalent to A fixed-for-fixed currency swap and one
interest rate swap
15. An interest rate swap has three years of remaining life. Payments are exchanged annually.
Interest at 3% is paid and 12-month LIBOR is received. A exchange of payments has just
taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 2%, 3% and
16.
17.
18.
19.
20.
4%. All rates an annually compounded. What is the value of the swap as a percentage of the
principal when LIBOR discounting is used. 2.66%
A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual
compounding) has a remaining life of nine months. The six-month LIBOR rate observed three
months ago was 4.85% with semi-annual compounding. Today’s three and nine month
LIBOR rates are 5.3% and 5.8% (continuously compounded) respectively. From this it can be
calculated that the forward LIBOR rate for the period between three- and nine-months is
6.14% with semi-annual compounding. If the swap has a principal value of $15,000,000,
what is the value of the swap to the party receiving a fixed rate of interest? -$70,760
Which of the following describes the way a LIBOR-in-arrears swap differs from a plain vanilla
interest rate swap? . Interest is paid at the beginning of the accrual period in a LIBOR-inarrears swap
In a fixed-for-fixed currency swap, 3% on a US dollar principal of $150 million is received and
4% on a British pound principal of 100 million pounds is paid. The current exchange rate is
1.55 dollar per pound. Interest rates in both countries for all maturities are currently 5%
(continuously compounded). Payments are exchanged every year. The swap has 2.5 years
left in its life. What is the value of the swap? -$9.15
Which of the following is a typical bid-offer spread on the swap rate for a plain vanilla
interest rate swap? 3 basis points
Which of the following describes the five-year swap rate? The rate that can be earned over
five years from a series of short-term loans to AA-rated companies
Chapter 8
1. Which of the following tends to lead to an increase in house prices? Banks reducing the
minimum FICO score that borrowers are required to have
2. Which of the following is true of a non-recourse mortgage? The house buyer has an
American-style put option on the house
3. Which of the following is NOT true Correlations decrease in stressed market conditions
4. Suppose that an ABS is created from a portfolio of subprime mortgages with the following
allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. Losses
on the mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are
losses on the mezzanine tranche of the ABS 60%
5. Suppose that ABSs are created from portfolios of subprime mortgages with the following
allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. (The
portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created
from the mezzanine tranches of the ABSs with the same allocation of principal. Losses on the
mortgage portfolio prove to be 16%. What, as a percent of tranche principal, are losses on
the mezzanine tranche of the ABS CDO 100%
6. Suppose that ABSs are created from portfolios of subprime mortgages with the following
allocation of the principal to tranches: senior 80%, mezzanine 10%, and equity 10%. (The
portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created
from the mezzanine tranches with the same allocation of principal. Losses on the mortgage
portfolio prove to be 16%. What, as a percent of tranche principal, are losses on the senior
tranche of the ABS CDO 50%
7. AIG lost money because It insured AAA tranches of ABS CDOs
8. Which of the following survived the crisis without declaring bankruptcy or being taken over
by another financial institution? Morgan Stanley
9. What are teaser rates Interest rates that apply only for the first two or three years
10. Which of the following describes the waterfall typically used for mortgages pre-crisis? A
distribution of cash flows to tranches with priority given to tranche with the highest rating
11. In 2008 the TED spread reached a high of about 450 basis points
12. Which of the following were introduced before the credit crisis that started in 2007 Basel II
13. Which of the following is true as the correlation between mortgage defaults increases?
Senior tranches become more likely to incur losses
14. Which of the following describes the S&P/Case-Shiller index? An index of house prices
15. Suppose that ABSs are created from portfolios of subprime mortgages with the following
allocation of the principal to tranches: senior 85%, mezzanine 10%, and equity 5%. (The
portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created
from the mezzanine tranches with the same allocation of principal. How high can losses on
the mortgages be before the mezzanine tranche of the ABD CDO bears losses? 5.5%
16. Suppose that ABSs are created from portfolios of subprime mortgages with the following
allocation of the principal to tranches: senior 85%, mezzanine 10%, and equity 5%. (The
portfolios of subprime mortgages have the same default rates.) An ABS CDO is then created
from the mezzanine tranches with the same allocation of principal. How high can losses on
the mortgages be before the senior tranche of the ABS CDO bears losses? 6.5%
17. Suppose that ABSs are created from portfolios of subprime mortgages with the following
allocation of the principal to tranches: senior 94.5% (rated AAA), mezzanine 0.1% (rated
BBB), and equity 5% (rated C) . The portfolios of subprime mortgages have the same default
rates. An ABS CDO is then created from the mezzanine tranches. Which of the following is
true? The ABS CDO tranches should all be rated BBB
18. Which of the following describes regulatory arbitrage? Finding a way of reducing capital
requirements without changing the risks being taken
19. Which of the following describes a subprime mortgage? The credit risk is high
20. Which of the following would be described by the term “liar loan”? A situation where the
borrower lied about the his or her income
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Chapter 9
Prior to the credit crisis that started in 2007 which of the following was used by derivatives
traders for the discount rate when derivatives were valued The LIBOR rate
Since the credit crisis that started in 2007 which of the following have derivatives traders
used as the risk-free discount rate for collateralized transactions The overnight indexed
swap rate
Which of the following is true OIS rates are less than the corresponding LIBOR/swap rates
Which of the following describes a 3-month overnight indexed swap (OIS)? The geometric
average of overnight rates is exchanged for a fixed rate at the end of three months
Suppose that OIS rates for all maturities are 2.5% and swap rates for all maturities are 3%.
Which of the following is true? Forward LIBOR rates are the same for both OIS discounting
and LIBOR discounting
CVA stands for Credit value adjustment
In a fully collateralized transaction which of the following leads to a pricing adjustment Both
B & C (The rate paid on cash collateral is greater than the fed funds rate & The rate paid on
cash collateral is less than the fed funds rate)
When a bank’s borrowing rate goes up, which of the following is true DVA increases so that
the bank’s profit goes up
In October 2008 the three-month LIBOR-OIS spread rose to 364 basis points
As a bank`s borrowing rate increases, which of the following is true if a bank calculates FVA
FVA increases
Which of the following is true CVA and DVA must both be calculated for the whole portfolio
a bank has with a counterparty
Which of the following is true when a bank uses OIS discounting for valuing a LIBOR-for-fixed
swap The OIS zero curve is calculated before the LIBOR/swap zero curve
13. It is assumed that a company can default after one year or after two years. The probability
of default at each time is 1.5%. The present value of the expected loss to a bank on a
derivatives portfolio if the company defaults after one year is estimated to be $1 million.
The present value of the expected loss if it defaults after two years is estimated to be $2
million. Which of the following is the bank’s CVA ? $45,000
14. Accountants like to value a derivatives portfolio at the exit price
15. In the U.S., which of the following is true about Treasury instruments Their income is not
subject to tax at the state level
16. Suppose that OIS rates of all maturities are 6% per annum, continuously compounded. The
one-year LIBOR rate is 6.4%, annually compounded and the two-year swap rate for a swap
where payments are exchanged annually is 6.8%, annually compounded. Which of the
following is closest to the LIBOR forward rate for the second year when LIBOR discounting is
used and the rate is expressed with annual compounding 7.229%
17. Suppose that OIS rates of all maturities are 6% per annum, continuously compounded. The
one-year LIBOR rate is 6.4%, annually compounded and the two-year swap rate for a swap
where payments are exchanged annually is 6.8%, annually compounded. Which of the
following is closest to the LIBOR forward rate for the second year when OIS discounting is
used and the rate is expressed with annual compounding? 7.225%
18. Which of the following involves most credit risk OTC trading with bilateral clearing and no
collateral being posted
19. A bank has three uncollateralized transactions with a counterparty worth +$10 million, −$20
million and +$25 million. A netting agreement is in place. What is the maximum loss if the
counterparty defaults today. $15 million
20. Since the 2008 credit crisis OIS has replaced LIBOR as the discount rate for collateralized
swap
Chapter 10
1. Which of the following describes a call option? The right to buy an asset for a certain price
2. Which of the following is true? None of the above (A long call is the same as a short put, A
short call is the same as a long put, A call on a stock plus a stock is the same as a put)
3. An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1
stock split. Which of the following is the position of the investor after the stock split? C. Put
options to sell 200 shares for $10
4. An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock
dividend. Which of the following is the position of the investor after the stock dividend? Put
options to sell 125 shares for $16
5. An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash
dividend. Which of the following is then the position of the investor? The investor has put
options to sell 100 shares for $20
6. Which of the following describes a short position in an option? A position where an option
has been sold
7. Which of the following describes a difference between a warrant and an exchange-traded
stock option? The number of warrants is fixed whereas the number of exchange-traded
options in existence depends on trading
8. Which of the following describes LEAPS? Exchange-traded stock options with longer lives
than regular exchange-traded stock options
9. Which of the following is an example of an option class? All calls on a certain stock
10. Which of the following is an example of an option series? All calls with a particular time to
maturity and strike price on a certain stock
11. Which of the following must post margin? The seller of an option
12. Which of the following describes a long position in an option? A position where an option
has been purchased
13. Which of the following is NOT traded by the CBOE? Monthlys
14. When a six-month option is purchased The price must be paid in full
15. Which of the following are true for CBOE stock options? The initial margin and maintenance
margin are determined by formulas and are equal
16. The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike
price of $70 when the option price is $4. The options are exercised when the stock price is
$69. What is the trader’s net profit or loss? Gain of $1,500
17. A trader buys a call and sells a put with the same strike price and maturity date. What is the
position equivalent to? A long forward
18. The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike
price of $60 when the option price is $10. When does the trader make a profit? When the
stock price is below $50
19. Consider a put option and a call option with the same strike price and time to maturity.
Which of the following is true? One of the options must be either in the money or at the
money
20. In which of the following cases is an asset NOT considered constructively sold? The owner
buys an in-the-money put option on the asset
Chapter 11
1. When the stock price increases with all else remaining the same, which of the following is
true? Calls increase in value while puts decrease in value
2. When the strike price increases with all else remaining the same, which of the following is
true? Puts increase in value while calls decrease in value
3. When volatility increases with all else remaining the same, which of the following is true?
Both calls and puts increase in value
4. When dividends increase with all else remaining the same, which of the following is true?
Puts increase in value while calls decrease in value
5. When interest rates increase with all else remaining the same, which of the following is
true? Calls increase in value while puts decrease in value
6. When the time to maturity increases with all else remaining the same, which of the
following is true? European options are liable to increase or decrease in value
7. The price of a stock, which pays no dividends, is $30 and the strike price of a one year
European call option on the stock is $25. The risk-free rate is 4% (continuously
compounded). Which of the following is a lower bound for the option such that there are
arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities
if it is above the lower bound? $5.98
8. A stock price (which pays no dividends) is $50 and the strike price of a two year European
put option is $54. The risk-free rate is 3% (continuously compounded). Which of the
following is a lower bound for the option such that there are arbitrage opportunities if the
price is below the lower bound and no arbitrage opportunities if it is above the lower
bound? $0.86
9. Which of the following is NOT true? (Present values are calculated from the end of the life of
the option to the beginning) An American put option is always worth less than the present
value of the strike price
10. Which of the following best describes the intrinsic value of an option? The value it would
have if the owner had to exercise it immediately or not at all
11. Which of the following describes a situation where an American put option on a stock
becomes more likely to be exercised early? The stock price volatility decreases
12. Which of the following is true? An American call option on a stock should never be exercised
early when no dividends are expected
13. Which of the following is the put-call parity result for a non-dividend-paying stock? The
European put price plus the stock price must equal the European call price plus the present
value of the strike price
14. Which of the following is true when dividends are expected? The basic put-call parity
formula can be adjusted by subtracting the present value of expected dividends from the
stock price
15. The price of a European call option on a non-dividend-paying stock with a strike price of $50
is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is
6% and the time to maturity is one year. What is the price of a one-year European put
option on the stock with a strike price of $50? $2.09
16. The price of a European call option on a stock with a strike price of $50 is $6. The stock price
is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to
maturity is one year. A dividend of $1 is expected in six months. What is the price of a oneyear European put option on the stock with a strike price of $50? $3.06
17. A European call and a European put on a stock have the same strike price and time to
maturity. At 10:00am on a certain day, the price of the call is $3 and the price of the put is
$4. At 10:01am news reaches the market that has no effect on the stock price or interest
rates, but increases volatilities. As a result the price of the call changes to $4.50. Which of
the following is correct? The put price increases to $5.50
18. Interest rates are zero. A European call with a strike price of $50 and a maturity of one year
is worth $6. A European put with a strike price of $50 and a maturity of one year is worth $7.
The current stock price is $49. Which of the following is true? None of the above (Both the
call and put must be mispriced, The put price is high relative to the call price, The call price is
high relative to the put price)
19. Which of the following is true for American options? Put-call parity provides an upper and a
lower bound for the difference between call and put prices
20. Which of the following can be used to create a long position in a European put option on a
stock? Buy a call on the stock and short the stock
Chapter 12
1. Which of the following creates a bull spread? Buy a low strike price call and sell a high strike
price call
2. Which of the following creates a bear spread? B. Buy a high strike price call and sell a low
strike price call
3. Which of the following creates a bull spread? Buy a low strike price put and sell a high strike
price put
4. Which of the following creates a bear spread? Buy a high strike price put and sell a low strike
price put
5. What is the number of different option series used in creating a butterfly spread? 3
6. A stock price is currently $23. A reverse (i.e short) butterfly spread is created from options
with strike prices of $20, $25, and $30. Which of the following is true? The gain when the
stock price is greater than $30 is the same as the gain when the stock price is less than $20
7. Which of the following is correct? A calendar spread can be created by buying a call and
selling a call when the strike prices are the same and the times to maturity are different
8. What is a description of the trading strategy where an investor sells a 3-month call option
and buys a one-year call option, where both options have a strike price of $100 and the
underlying stock price is $75? Bullish Calendar Spread
9. Which of the following is correct? A diagonal spread can be created by buying a call and
selling a call when the strike prices are different and the times to maturity are different
10. Which of the following is true of a box spread? All of the above (It involves two call options
and two put options, It has a known value at maturity, It is a package consisting of a bull
spread and a bear spread)
11. How can a straddle be created? Buy one call and one put with the same strike price and
same expiration date
12. How can a strip trading strategy be created? Buy one call and two puts with the same strike
price and expiration date
13. How can a strap trading strategy be created? Buy two calls and one put with the same strike
price and expiration date
14. How can a strangle trading strategy be created? Buy one call and one put with different
strike prices and same expiration date
15. Which of the following describes a protective put? A long put option on a stock plus a long
position in the stock
16. Which of the following describes a covered call? A short call option on a stock plus a long
position in the stock
17. When the interest rate is 5% per annum with continuous compounding, which of the
following creates a principal protected note worth $1000? A one-year zero-coupon bond
plus a one-year call option worth about $49
18. A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by
trading a total of 400 options. The options are worth $11, $14, and $18. What is the
maximum net gain (after the cost of the options is taken into account)? $400
19. A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by
trading a total of 400 options. The options are worth $11, $14, and $18. What is the
maximum net loss (after the cost of the options is taken into account)? $100
20. Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is
the maximum gain when a bull spread is created by trading a total of 200 options? $300
Chapter 13
1. 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. An investor sells sixmonth call options with a strike price of $32. Which of the following hedges the position?
Buy 0.4 shares for each call option sold
2. 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. What is the riskneutral probability of that the stock price will be $36? 0.4
3. 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. An investor sells call
options with a strike price of $32. What is the value of each call option? $1.6
4. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to
rise to $42 or fall to $37. An investor buys one-year put options with a strike price of $41.
Which of the following is necessary to hedge the position? Buy 0.8 shares for each option
purchased
5. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to
rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the
value of each option? The risk-free interest rate is 2% per annum with continuous
compounding. $0.93
6. Which of the following describes how American options can be valued using a binomial tree?
Check whether early exercise is optimal at all nodes where the option is in-the-money
7. In a binomial tree created to value an option on a stock, the expected return on stock is the
risk-free rate
8. In a binomial tree created to value an option on a stock, what is the expected return on the
option? Risk-free rate
9. A stock is expected to return 10% when the risk-free rate is 4%. What is the correct discount
rate to use for the expected payoff on an option in the real world? It could be more or less
than 10%
10. Which of the following is true for a call option on a stock worth $50 As a stock’s expected
return increases the price of the option on the stock stays the same
11. Which of the following are NOT true A hedge set up to value an option does not need to be
changed
12. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a
European call option on the stock with a strike price of $32 that expires in 6 months. Each
step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is
the option price when u = 1.1 and d = 0.9? $1.49
13. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a
European put option on the stock with a strike price of $32 that expires in 6 months with u =
1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%. $2.24
14. Which of the following is NOT true in a risk-neutral world? Investors expect higher returns to
compensate for higher risk
15. If the volatility of a non-dividend paying stock is 20% per annum and a risk-free rate is 5%
per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a
tree with a three-month time step? 1.11
16. If the volatility of a non-dividend-paying stock is 20% per annum and a risk-free rate is 5%
per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a
tree with a three-month time step? 0.54
17. The current price of a non-dividend paying stock is $50. Use a two-step tree to value an
American put option on the stock with a strike price of $48 that expires in 12 months. Each
step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the
following is the option price? $2.00
18. Which of the following describes delta? The ratio of a change in the option price to the
corresponding change in the stock price
19. When moving from valuing an option on a non-dividend paying stock to an option on a
currency which of the following is true? The risk-free rate is replaced by the excess of the
domestic risk-free rate over the foreign risk-free rate when p is calculated
20. A tree is constructed to value an option on an index which is currently worth 100 and has a
volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to
value an option on a non-dividend-paying stock which is currently worth 100 and has a
volatility of 25%. Which of the following are true? The parameter u is the same for both
trees but p is not
Chapter 15
1. Which of the following is assumed by the Black-Scholes-Merton model? The stock price at a
future time is lognormal
2. The original Black-Scholes and Merton papers on stock option pricing were published in
which year? 1973
3. Which of the following is a definition of volatility The standard deviation of the return,
measured with continuous compounding, in one year
4. A stock price is $100. Volatility is estimated to be 20% per year. What is an estimate of the
standard deviation of the change in the stock price in one week? $2.77
5. What does N(x) denote? B. The area under a normal distribution up to x
6. Which of the following is true for a one-year call option on a stock that pays dividends every
three months? None of the above. (It can be optimal to exercise the option at any time, It is
only ever optimal to exercise the option immediately after an ex-dividend date, It is never
optimal to exercise the option early)
7. What is the number of trading days in a year usually assumed for equities? 252
8. The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%.
Which of the following is a way of valuing a derivative? Assuming that the expected growth
rate for the stock price is 5% and discounting the expected payoff at 5%
9. When there are two dividends on a stock, Black’s approximation sets the value of an
American call option equal to which of the following The greater of the value in B and the
value assuming no early exercise
10. Which of the following is measured by the VIX index Implied volatilities for options trading
on the S&P 500 index
11. What was the original Black-Scholes-Merton model designed to value? A European option
on a stock providing no dividends
12. A stock provides an expected return of 10% per year and has a volatility of 20% per year.
What is the expected value of the continuously compounded return in one year? 8%
13. An investor has earned 2%, 12% and -10% on equity investments in successive years
(annually compounded). This is equivalent to earning which of the following annually
compounded rates for the three year period. 0.93%
14. Which of the following is NOT true? Risk-neutral valuation provides prices that are only
correct in a world where investors are risk-neutral
15. Which of the following is a way of extending the Black-Scholes-Merton formula to value a
European call option on a stock paying a single dividend? Subtract the present value of the
dividend from the stock price
16. When the Black-Scholes-Merton and binomial tree models are used to value an option on a
non-dividend-paying stock, which of the following is true? The binomial tree price converges
to the Black-Scholes-Merton price as the number of time steps is increased
17. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is
6%, the volatility is 20% and the time to maturity is 3 months which of the following is the
price of a European call option on the stock 20N(0.2)-19.7N(0.1)
18. When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is
6%, the volatility is 20% and the time to maturity is 3 months which of the following is the
price of a European put option on the stock 19.7N(-0.1)-20N(-0.2)
19. A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is
closest to the volatility per annum estimated from this data? 80%
20. The volatility of a stock is 18% per year. Which of the following is closest to the volatility per
month? 5.2%
158.505
4.864
140.000
14.547
123.656
24.872
179.455
0.00
140.000
10.000
109.220
40.780