A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.
If settled at the time of borrowing, what amount would the borrower pay or receive on a
$500,000 loan if the prevailing 6-month interest rate is 2.9%?
A) $1,000 payment
B) $1,000 receipt
C) $972 payment
D) $972 receipt
The price of a 6-month T-bill is 96.73. You wish to enter into a repurchase agreement
that provides for your purchase of a $100,000 bond in 10 days at a price of 97.02. What
is the implied 10 day repo rate in this transaction?
A) 0.10%
B) 0.20%
C) 0.30%
D) 0.40%
The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0%
and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the
volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce
indefinitely, what is the value of the unopened well?
A) $724
B) $854
C) $913
D) $1,025
What term is sometimes used to describe the price at a particular point in time, say
maturity, that is necessary to calculate today’s price?
A) Face value
B) Par value
C) Boundary condition
D) All of the above
Mary wagers to pay one share of stock to Matt if the price at expiration in 1 year is
above $75.00. Assume S(0) = 60.00, σ = 0.15, r = 0.04, and dividend rate = 0.01. What
is the value of Mary’s bet?
A) $6.55
B) $7.55
C) $8.55
D) $9.55
Two 6-month corn put options are available. The strike prices are $1.80 and $1.75 with
premiums of $0.14 and $0.12, respectively. Total costs are $1.65 per bushel and
6-month interest rates are 4.0%. Farmer Jayne wishes to hedge 20,000 bushels for 6
months. What is the highest profit or minimum loss between the two options if the spot
price in 6 months is $1.70 per bushel?
A) $88 loss
B) $88 gain
C) $496 loss
D) $496 gain
Bonds maturing in 1, 2, and 3 years have prices of 0.9323, 0.8762, and 0.8002,
respectively. A 0.8900 call on a 1-year bond matures in 1 year with σ = 0.25. What is
the price of a 10.0% interest rate caplet that expires in 1 year?
A) $0.50
B) $0.60
C) $0.70
D) $0.80
An existing well is operating and the price of oil is $115 per barrel. The effective lease
rate and risk free rate are 3.0% and 4.0%, respectively. The constant cost of extraction
is $85 per barrel and the volatility of prices is 15.0%. If it costs nothing to shut down
the well, at what price would we close the well?
A) $41
B) $48
C) $52
D) $59
Assume S = $31.75, div = 0, r = 0.03, and σ = 0.20, and 90 days until the expiration of a
standard call option. A call on call compound option with an exercise price of $2.00 has
180 days until expiration. What is the premium of the call on call option?
A) $1.46
B) $2.46
C) $3.04
D) $3.53
The S&P 500 Index price is $925.28 and its annualized dividend yield is 1.40%. LIBOR
is 4.2%. How many futures contracts will you need to hedge a $25 million portfolio
with a beta of 0.9 for one year?
A) 105
B) 120
C) 80
D) 95
A bond has a current value of $950 and promises to pay $1,000 at the end of 4 years.
The expected return on the asset is 12% and the risk free rate is 3%. If the actual cash
payout in case of default is 0, what is the risk neutral default probability given that the
asset has a standard deviation of 18%?
A) 15.2%
B) 21.5%
C) 33.2%
D) 49.6%
The spot price of the market index is $900. A 3-month forward contract on this index is
priced at $930. What is the profit or loss to a short position if the spot price of the
market index rises to $920 by the expiration date?
A) $20 gain
B) $20 loss
C) $10 gain
D) $10 loss
Jessie, Inc. has 4-year zero-coupon bonds outstanding, which will pay $1,000 at
maturity. The assets are valued at $900, σ = 0.25, r = 0.045, and the company does not
pay a dividend. Using a Black-Scholes model, what is the yield on debt?
A) 4.68%
B) 6.48%
C) 8.46%
D) 8.64%
Walla, Inc. may invest $6 million in a Buffalo harvesting project. Annual costs and
revenues, starting next year, are forecasted to be $1 million and $0.7 million, growing at
0.0% and 3.0%, respectively. If the opportunity cost of capital is 4.5%, what is the
investment trigger price?
A) $19.25 million
B) $21.25 million
C) $23.25 million
D) $25.25 million
What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock
pays a 1.0% continuous dividend and the option expires in 110 days?
A) $2.70
B) $2.10
C) $1.80
D) $1.20
The price of oil is $115 per barrel. The effective lease rate and risk free rate are 3.0%
and 4.0%, respectively. The constant cost of extraction is $85 per barrel and the
volatility of prices is 15.0%. If an untapped well costs $2,100 to open and can produce
indefinitely, at what price per barrel should the well be opened?
A) $349
B) $423
C) $454
D) $484
Which of the following is not commonly used as a numeraire?
A) Futures contract
B) Money market account
C) Risky asset
D) Zero coupon bond
Consider a three-period binomial model of 12 months. Assume the stock price is
$37.50,
σ = 0.20, r = 0.05 and the exercise price of a call option is $35. What is the forecasted
price of the stock at the node after two consecutive upward movements of the stock
price?
A) $38.68
B) $42.80
C) $48.84
D) $50.06
Assume a stock price of S(0) = $62.00, r = 0.05, σ = 0.30, and dividend = 0. What is the
price of a claim that pays ? Use formula 20.29.
A) $7.59
B) $8.59
C) $9.59
D) $10.59
The deterministic drift of a pure Brownian motion that is virtually undetectable is
sometimes referred to as the:
A) Distribution
B) Expected return
C) Random walk
D) Standard deviation
Consider a one-period binomial model of 6 months. Assume the stock price is $63.00,
σ = 0.28, r = 0.05 and the stock’s expected return is 14.0%. What is the true probability
of the stock going up?
A) 56.6%
B) 52.4%
C) 48.2%
D) 46.4%
What is the area under the standard normal distribution curve and is less than 0.654?
A) 0.5115
B) 0.6215
C) 0.7434
D) 0.8283
Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous
dividend. Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given
an immediate price increase of $1.50?
A) 24.61
B) 18.61
C) 14.61
D) 9.61
Two months from today you plan to borrow $3 million for 6 months at LIBOR. You
hedge your interest rate risk with a euro dollar futures contract priced at 93.6. If settled
in arrears, what is your payment if the 6-month LIBOR is 2.5% in two months?
A) $8,500
B) $10,500
C) $13,500
D) $15,500
The spot exchange rate of dollars per euro is 0.95. Dollar and euro interest rates are
7.0% and 6.0%, respectively. The price of a $0.93 strike 6-month call option is $0.08.
What is the price of the put?
A) $0.016
B) $0.032
C) $0.056
D) $0.078
Which of the following examples does not involve different numeraire?
A) Currency translation
B) Quantity uncertain
C) Backward equation
D) All-or-nothing options
Assume that an investor lends 100 shares of Jiffy, Inc. common stock to a short seller.
The bid-ask prices are $32.00 – $32.50. When the position is closed, the bid-ask prices
are
$32.50 – $33.00. The commission rate is 0.5%. The market interest rate is 5.0% and the
short rebate rate is 3.0%. Calculate the gain or loss to the lender. Assume the lender is
not subject to a bid-ask loss or commissions.
A) $164.00 gain
B) $164.00 loss
C) $100.00 gain
D) $100.00 loss
Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68
days until expiration. Under a delta hedge position, what is your overnight profit/loss if
the stock rises to $34.50?
A) $9.23 loss
B) $9.23 gain
C) $7.62 loss
D) $7.62 gain
What is the delta on a $20 strike call? Assume S = $22.00, σ = 0.30, r = 0.05, the stock
pays a 1.0% continuous dividend and the option expires in 80 days?
A) 0.790
B) 0.820
C) 0.850
D) 0.880
A Brownian motion is a stochastic process that can be described as a:
A) Pattern of movements with continuous movements
B) Pattern of movements with discrete movements
C) Random walk with continuous movements
D) Random walk with discrete movements
Who from the following list would be considered a speculator by entering into a futures
or options contract on commodities?
A) Farmer
B) Corn delivery truck driver
C) Food manufacturer
D) None of the above
What is the pure yield curve and why is it common to present coupon-based yield
curves in practice?
Why is the perpetual call formula used to price commodity extraction options?
How does the existence of swaptions add to the possibilities in risk management
techniques?
Name some advantages that futures contracts have over forward contracts.
Why might normally distributed returns appear non-normal?
Why might a down-and-in put option be more attractive than a standard option when
hedging a foreign currency position?
When hedging a foreign currency position, what makes a down-and-out put
unattractive?
In the first-order condition for portfolio selection, explain the meaning of equilibrium.
Why does an Asian option benefit from a larger number of draws in a Monte Carlo
simulation?
What is the one aspect of volatility that is assumed in the Black-Scholes model and why
might that assumption be in error?
Why would a manufacturer elect to use a long call strategy instead of a forward contract
to hedge the risk associated with variable costs?
What aspect of risk-neutral pricing valuation links it to portfolio selection?
What is calibration?
Briefly define a terminal boundary condition.
What is the process involved in creating a cash-and-carry strategy?
Why is a straddle position considered a speculation on the asset’s volatility?
Which Greek is also called time decay and why?