Assume S = $42, K = 45, div = 0, r = 0.04, σ = 0.48, and 80 days until expiration. What
is the premium on a knock-out put option with a down-and-out barrier of $44?
A) $2.13
B) $3.13
C) $3.47
D) $4.07
Jafee Corp. common stock is priced at $36.50 per share. The company just paid its
$0.50 quarterly dividend. Interest rates are 6.0%. A $35.00 strike European call,
maturing in 6 months, sells for $3.20. What is the price of a 6-month, $35.00 strike put
option?
A) $1.20
B) $1.64
C) $2.04
D) $2.38
Corn call options with a $1.75 strike price are trading for a $0.14 premium. Farmer
Jayne decides to hedge her 20,000 bushels of corn by selling short call options.
Six-month interest rates are 4.0% and she plans to close her position in 6 months. What
is the total premium she will earn on her short position?
A) $2,800
B) $2,912
C) $800
D) $1,600
Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8,
what is the risk neutral default probability?
A) 13.0%
B) 20.5%
C) 38.3%
D) 44.4%
Use VaR techniques to determine the cost of insurance on a risky investment. The
investment asset has a value of $80 and pays no dividend. The historical standard
deviation of the asset is 15% and the expected return on the asset is 8%. At the 95%
confidence level, what is the price of a put option that insures the asset over the next
year?
A) $2.56
B) $1.25
C) $0.86
D) $0.15
Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6
months (180 days). The standard deviation of the stock is 0.25 and the risk free interest
rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. At
approximately what stock price will the wager be of equal value to both Joe and Sarah?
A) $32.00
B) $33.30
C) $34.25
D) $35.00
Plotting the volatility of a security in a three dimensional graph, using time to maturity
on one axis and strike price on another, is referred to as volatility:
A) Skew
B) Smile
C) Smirk
D) Surface
Assume S = $48.35, K = 45, σ = 0.23, r = 0.04, T – t = 60 days, div = 0, and a jump
probability = 0.005. What is the increase in the value of a call over a no-jump call?
A) $0.04
B) $0.03
C) $0.02
D) $0.01
For a stock price that was initially $55.00, what is the price after 4 years if the
continuously compounded returns for these 4 years are 4.5%, 6.2%, 8.9%, -3.2%?
A) $64.80
B) $74.80
C) $84.80
D) $94.80
A stock has a price of $42.63 and pays no dividend. The historical standard deviation of
the stock is 18% and the expected return on the stock is 11%. At the 95% confidence
level, what is the Tail VaR over the next 270 days?
A) $2.13
B) $6.56
C) $9.71
D) $40.50
A company issues an option grant with an outperformance feature, against the S&P 500.
Assume S&P 500 = 1100, S = 46, k = 45, σ = 0.30, r = 0.04, and 10 years until
expiration. The S&P 500 has a dividend yield of 2.5%, standard deviation of 20.0% and
a 0.45 correlation coefficient with the stock. What is the value of the outperformance
option?
A) $11.92
B) $15.99
C) $19.75
D) $21.05
The Buckingham Casino offers to give every gambler one share of Buckingham Casino
Corp. stock if the price drops below $40.00, as an incentive to spur business. If S =
$45.25, σ = 0.15,
r = 0.05 and div = 0, how much profit or loss is Buckingham incurring if they charge
$0.25 to participate in this wager?
A) $0.31 loss
B) $0.31 profit
C) $0.19 loss
D) $0.19 profit
A multivariate option that has a claim with a payoff determined by the average of two
or more asset prices is known as:
A) Basket options
B) Multioptions
C) Quantos options
D) Rainbow options
The price of a 3-year zero coupon government bond is 85.16. The price of a similar
4-year bond is 79.81. What is the yield to maturity (effective annual yield) on the 4-year
bond?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
What method uses the insight that for each simulated realization there is an opposite
and equally likely realization?
A) Stratified sampling
B) Control variate
C) Antithetic variate
D) Efficient variate
Describe the true relationship between option prices and delta. Use calls as an example.
A company is forecasted to pay dividends of $0.90, $1.20, and $1.45 in 3, 6, and 9
months, respectively. Given interest rates of 5.5%, how much dollar impact will
dividends have on option prices? (Assume a 9-month option.)
A) $3.45
B) $3.90
C) $4.22
D) $4.50
Assume a stock price of S(0) = $80.00, r = 0.05, σ = 0.35, and dividend = 0.01. What is
the price of a claim that pays S-2/3? Use formula 20.29.
A) $0.25
B) $0.35
C) $0.05
D) $0.15
Assume S = $66, K = 65, div = 0, r = 0.04, σ = 0.25, and 60 days until expiration. What
is the premium on a knock-out call option with a down-and-out barrier of $60?
A) $2.40
B) $2.70
C) $3.00
D) $3.30
The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50. The
observed futures price is 97.5 and the YTM is 5.8%. What is invoice less market price
on the security?
A) +0.08
B) -0.08
C) -0.02
D) +0.02
When the volatility of an asset is higher at the deep in the money and deep out of the
money positions, than at the money, the plot is called a volatility:
A) Skew
B) Smile
C) Smirk
D) Surface
Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock
price is $61.00. What is the theta of the option as the expiration time declines from 60
to 50 days?
A) -0.52
B) -0.42
C) -0.32
D) -0.22
What is the maximum loss that an investor can obtain over 6 months from a strategy
employing a long 830 call and a short 850 call? Interest rates are 0.5% per month.
A) $6.80
B) $7.68
C) $9.24
D) $12.32
Assume a stock price of S(0) = $45.00, r = 0.03, σ = 0.40, and dividend = 0.015. What
is the price of a claim that pays ? Use formula 20.29.
A) $6.41
B) $5.41
C) $4.41
D) $3.41
A bond maturing in 5 years has a YTM = 0.065 and an annual yield volatility of 2.0%.
Given a $15 million portfolio, what is the value at risk over 2 weeks at a 95%
confidence level?
A) $283,917
B) $383,917
C) $483,917
D) $583,917
The risk-neutral measure arises when we select ________ as the numeraire.
A) Asset portfolio
B) Corporate bond
C) Treasury bond
D) Money market account
Farmer Jayne bought a $1.70 strike put option for $0.11 and sold a $1.75 strike call
option for a premium of $0.14. Her total costs are $1.65 per bushel and interest rates are
4.0% over this period. What is the floor in her strategy assuming a 20,000-bushel crop?
A) $624
B) $1,624
C) $2,624
D) $3,624
Refer to the table 6.1. Which of the following terms most accurately describes the
forward curve for soybeans over the next two years?
A) Contango
B) Backwardation
C) Contango and backwardation
D) None of the above
For a utility function that exhibits decreasing martingale utility, the martingale utility is
high when:
A) Consumption and utility are low
B) Consumption and utility are high
C) Consumption is low and utility is high
D) Consumption is high and utility is low
The Buckingham Casino offers to give every gambler one share of Buckingham Casino
Corp. stock if the price drops below $40.00, as an incentive to spur business. If S =
$45.25, σ = 0.15,
r = 0.05 and div = 0, how much is this offer worth if it expires in 30 days?
A) $0.36
B) $0.26
C) $0.16
D) $0.06
A 4-year bond with a price of 100.696 exists. The duration on the bond is 3.674. If the
yield rises from 5.8% to 6.2%, what is the new bond price as estimated by the duration?
A) $98.40
B) $99.30
C) $100.60
D) $101.40
How do probabilities change with a change of measure?
Why do we assume a lognormal distribution in option pricing?
What is the rationale behind cheapest-to-deliver calculations and why do we perform
such calculations?
Explain the relationship between options costs and profits under a put option insurance
strategy.
What are some uses for index futures contracts?
What possible tax advantage exists in equity-linked notes?
Explain the pattern of implied volatility that is often referred to as a smirk. (Use a call
as your example.)
When developing a binomial tree model where stocks pay discrete dividends, what
problem may occur?
Donald Trump offers to give you a partnership share in his casinos if the price of his
shares drops below a certain level. He charges a nominal fee for this right. What is he
offering you and is he wise?
Describe the concept of a bid-ask spread and how that impacts the cash flows of an
investor.
What does a transition matrix indicate about a bond’s future credit risk?
In a binomial pricing model, what is the lowest price of an option at any node and why?
Explain in simple terms why a call option on a non-dividend paying stock should never
be exercised early.
How would a market-maker hedge a swap involving variable price and quantity?