Consider a one-period binomial model of 6 months. Assume the stock price is $45.00,
σ = 0.20, r = 0.06 and the stock’s expected return is 12.0%. What is the discount rate for
a
$45.00 strike European call option (Y)?
A) 38.2%
B) 39.1%
C) 42.5%
D) 45.6%
Corn call options with a $1.70 strike price are trading for a $0.15 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 and sell her corn in
6 months. What is her profit or loss if spot prices are $1.60 per bushel when she closes
her position?
A) $1,000 loss
B) $2,000 gain
C) $2,120 loss
D) $2,120 gain
The current price of silver is $ 31.00 per ounce. The effective lease rate and risk free
rate are 1.0% and 3.5%, respectively. If the cost to mine one ounce of silver is a
constant $25.00, what is the value of an option to wait and mine the silver later?
A) $13.50
B) $14.50
C) $15.50
D) $16.50
We will assume that Nathans, Inc. has 3-year zero-coupon debt outstanding, which will
pay $200 at maturity. The assets are valued at $175, σ = 0.20, r = 0.04, and the company
does not pay a dividend. Using a Black-Scholes model, what is the value of the equity?
A) $23.05
B) $43.05
C) $63.05
D) $83.05
Suppose that B = $500 and A0 = $470, α = 9%, r = 4%, σ = 17%, and δ = 0. If T = 8,
what is the recovery rate assuming true default probability?
A) $369
B) $400
C) $470
D) $500
The spot price of the market index is $900. A 3-month forward contract on this index is
priced at $930. The annual rate of interest on treasuries is 2.4% (0.2% per month). What
annualized rate of interest makes the net payoff zero? (Assume monthly compounding.)
A) 4.8%
B) 8.5%
C) 11.2%
D) 13.2%
Assume a stock price of S(0) = $83.00, r = 0.045, σ = 0.25, and dividend = 0.02. What
is the price of a claim that pays S3? Use formula 20.29.
A) $423,323
B) $710,695
C) $624,165
D) $818,123
It can be said that Girsanov’s theorem shows the equivalence of which two items?
A) Change of drift and change of measure
B) Change of numeraire and change of measure
C) Change of drift and change of numeraire
D) Change of numeraire and change of process
A commodity linked bond is issued with an embedded call option. The current
commodity price is $52, as is the exercise price on the call option. The call option is
priced at $5.56. If the promised payment on the bond is the same as the issue price of
$40, what is the yield on the bond if effective interest rates are 4.0% and the bond has a
1-year maturity?
A) 2.24%
B) 2.80%
C) 3.50%
D) 4.0%
Consider a two-period binomial model, where each period is 6 months. Assume the
stock price is $75.00, σ = 0.35, and r = 0.05. An American call option with a strike price
of $80 would be exercised early at what dividend yield?
A) 5.0%
B) 7.0%
C) 9.0%
D) Never exercise early
What is the price of a $35 strike call? Assume S = $38.50, σ = 0.25, r = 0.06, the stock
pays no dividend and the option expires in 45 days.
A) $3.50
B) $3.65
C) $3.80
D) $3.95
What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock
pays a 2.0% continuous dividend and the option expires in 40 days?
A) 0.582
B) 0.602
C) 0.662
D) 0.702
The price of oil is $120 per barrel. The effective lease rate and risk free rate are 5.0%
and 6.0%, respectively. The constant cost of extraction is $105 per barrel and the
volatility of prices is 18.0%. What is the value of an option to defer extraction?
A) $30.68
B) $32.08
C) $34.56
D) $38.34
Assume oat spot prices over the next 3 years are $2.20, $2.35, and $2.28, respectively.
The original swap price was $2.30 per bushel. If cash settlement occurs, what
transaction will the counter-party make in year 2 on a 5,000-bushel swap agreement?
A) $250 payment
B) $250 receipt
C) $100 payment
D) $100 receipt
You own two bonds; 25% of a 30-year bond with σ = 0.02 and 75% of a 20-year bond
with
σ = 0.015. The correlation coefficient is 0.82. What is the 2-week value at risk at a 95%
confidence level? (Assume portfolio value = $15 million.)
A) $0
B) $234,357
C) $734,357
D) $1,734,357
Lechno, Inc. issues compensation options with the following terms. Strike = $65,
price = $63.50, σ = 0.22, r = 0.045, div = 0.015. What is the value of the option if it will
be repriced at $40? Assume 10 years to expiration.
A) $18.64
B) $22.22
C) $24.32
D) $26.84
The spot exchange rate in dollars per euro is $1.31. Dollar denominated interest rates
are 4.0% and euro denominated interest rates are 3.0%. What is the difference in call
and put option prices given a 2-year option and a $1.34 strike price?
A) -$0.1041
B) -$0.0652
C) $0.1233
D) $0.1546
Dawn, Inc. stock is $37.00 per share. The company’s semi-annual dividend is forecasted
as $0.25 per share, increasing every 6 months by 20.0%. What is the price of a
zero-coupon equity-linked bond, promising to pay one share in 4 years, given annual
interest rates of 6.0%?
A) $32.29
B) $33.49
C) $34.39
D) $35.69
A strategy consists of longing a put on the market index with a strike of 830 and
shorting a call option on the market index with a strike price of 830. The put premium is
$18.00 and the call premium is $44.00. Interest rates are 0.5% per month. What is the
breakeven price of the market index for this strategy at expiration (in 6 months)?
A) $802.12
B) $830.00
C) $855.21
D) $866.32
Assume S = $46, K = 45, div = 0, r = 0.03, σ = 0.20, and 50 days until expiration. What
is the premium on a knock-out put option with an up-and-out barrier of $50?
A) $0.83
B) $0.93
C) $1.13
D) $1.33
The spot price of the market index is $900. A 3-month forward contract on this index is
priced at $930. The market index rises to $920 by the expiration date. The annual rate
of interest on treasuries is 2.4% (0.2% per month). What is the difference in the payoffs
between a long index investment and a long forward contract investment? (Assume
monthly compounding.)
A) $10.84
B) $24.59
C) $26.40
D) $43.20
During periods when measured volatility is high, the typical day tends to exhibit high
volatility. This behavior is referred to as volatility:
A) Clustering
B) EWMA
C) Smile
D) Stochasticity
You wish to create a synthetic forward rate agreement in which you would lock in a
return between 150 and 310 days. The price of a 150-day zero coupon bond is 0.9823
and the price of 310-day zero coupon bond is 0.9634. What is the approximate yield on
the synthetic FRA?
A) 1.8%
B) 2.0%
C) 2.9%
D) 3.8%
Consider a two-period binomial model, where each period is 6 months. Assume the
stock price is $50.00, σ = 0.20, r = 0.06 and the dividend yield = 3.5%. What is the
lowest strike price where early exercise would occur with an American put option?
A) $50
B) $55
C) $60
D) $65
What is the payoff on a 75 strike Asian option given it is a geometric average price call?
The recent prices are 72, 76, 74, 78, and 78.
A) 0.46
B) 0.56
C) 0.66
D) 0.76
The concept created by Hakannson in 1976 to describe the exotic option like payoffs
that could result without the need for a delta hedging requirement is known as:
A) Exotics
B) Multioptions
C) Quantos
D) Supershares
Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar
denominated pound put is $1.20. Assume r = 0.04, rf = 0.05, σ = 0.20 and the option
expires in 270 days. What is the put option price?
A) $0.075
B) $0.085
C) $0.095
D) $0.105
The current price of silver is $32.00 per ounce. The effective lease rate and risk free rate
are 3.0% and 4.0%, respectively. If the cost to mine one ounce of silver is a constant
$25.00, what is the trigger price per ounce at which the silver will be mined?
A) $33.17
B) $35.17
C) $37.17
D) $39.17
A stock owned by a portfolio has a bankruptcy probability of 1% per year. Using a
Poisson distribution, what is the probability that this firm will not declare bankruptcy
over the upcoming 10 years?
A) 60%
B) 70%
C) 80%
D) 90%
A stock is currently selling for $22.00 per share. Ignoring interest, determine the
intrinsic value of a call option should there exist equally probable stock prices of $25.00
and $23.00.
A) $0.00
B) $1.00
C) $2.00
D) $3.00
A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a
standard deviation of 24.0%. What is the forecasted up movement in the stock over 6
months, assuming two periods of 3 months each?
A) $64.96
B) $69.69
C) $73.48
D) $76.96
Refer to the table 6.1. Given a lease rate of 7.0% on the 24-month corn forward
contract, what is the approximate potential arbitrage profit per contract?
A) 3.68 cents
B) 4.48 cents
C) 5.84 cents
D) 6.90 cents
Given zero-coupon bond yields are 2.0%, 2.5%, and 2.8% in years 1, 2, and 3,
respectively, calculate the prepaid swap price for corn. Assume corn forward prices for
the proceeding 3 years are $5.00, $5.20, and $5.35, respectively.
A) $14.87
B) $15.04
C) $16.12
D) $16.20
The 6-month call and put premiums are $0.114 and $0.098, respectively, with a $0.94
strike. Dollar and euro interest rates are 7.0% and 6.0%, respectively. What spot
exchange rate is implied by this data?
A) $0.98 dollars per euro
B) $1.02 dollars per euro
C) $1.05 dollars per euro
D) $1.09 dollars per euro
What is the difference in the expected returns on equity when using a Black-Scholes
formula versus a traditional weighted average formula? Assume rA = 0.12, rf = 0.06,
asset value = $170, equity value = $45, debt to value ratio = 0.55, and delta = 0.6500.
A) 1.00%
B) 1.20%
C) 1.40%
D) 1.60%