Suppose the 180-day futures price on crude oil is $110.00 per barrel and the volatility is
20.0%. Assume interest rates are 3.5%. What is the price of a $120 strike call futures
option that expires in 180 days?
A) $1.89
B) $2.19
C) $2.59
D) $3.09
Your $1 million portfolio consists of 50% of Jacko with = 0.14, σ = 0.20 and 50% of
Macko with = 0.10, σ = 0.15. The correlation coefficient is 0.25. What is the value at
risk over 1 week at a 95% confidence level?
A) $23,447
B) $26,447
C) $29,447
D) $32,447
The spot price of corn is $5.82 per bushel. The opportunity cost of capital for an
investor is 0.6% per month. If storage costs of $0.03 per bushel per month are factored
in, all else being equal, what is the future value of storage costs over a 6-month period?
A) $0.1534
B) $0.1684
C) $0.1772
D) $0.1827
What is the payoff on a 90 strike Asian option given it is a geometric average price put?
The recent prices are 89, 90, 91, 87, 87, and 88.
A) 1.25
B) 1.35
C) 1.45
D) 1.55
In a specific wager, Pat is paid $5.00 if the price of ABC Corp. is above $85.00.
Currently, ABC Corp. price is $75.00, σ = 0.25, r = 0.04, div = 0 and the wager lasts 6
months. Pat receives nothing if the price is below $85.00. What is the value of her
wager?
A) $1.20
B) $2.20
C) $3.20
D) $4.20
Put options with strikes of $70, $75, and $85 have option premiums of $6.00, $8.50,
and $11.00, respectively. Using strike price convexity, which option premium, if any, is
not possible?
A) P (70)
B) P (75)
C) P (85)
D) All are possible
Assume S = $60, K = $65, σ = 0.15, r = 0.05, T – t = 122 days, div = 0.015, and a jump
probability = 0.003. What is the value of a call?
A) $0.67
B) $1.67
C) $2.67
D) $3.67
A $1.75 strike call option has a $0.14 premium. The $1.75 strike put option premium is
$0.12. What is the net cost for Farmer Jayne to create a synthetic short forward
contract? (Assume 4.0% interest.)
A) $0.0208
B) -$0.0208
C) $0.000
D) -$0.0424
A modification to the Brownian process in which the drift and volatility depend on the
stock price is called:
A) Ornstein-Uhlenbeck
B) Diffusion
C) Ito
D) Geometric
Assume that an investor is currently holding a reverse straddle position (i.e. a short put
and short call), which is currently a profitable investment. All else being equal, what
would this investor like to happen to vega?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
What is the probability that a number drawn from the standard normal distribution will
be between -0.60 and 0.45?
A) 0.40
B) 0.50
C) 0.60
D) 0.70
When valuing options using true probabilities, the discount rate is computed as follows:
A) Once using the risk-free rate
B) At the final period
C) For each node
D) For each path
KMW, Inc. plans to pay a dividend of $0.50 per share both 3 and 6 months from today.
KMW’s share price today is $36.00 and the continuously compounded quarterly interest
rate is 1.5%. What is the price of a 6-month prepaid forward contract, which expires
immediately after the second dividend?
A) $35.00
B) $35.02
C) $36.98
D) $37.00
Given a mean of -4.3 and a standard deviation of 26, what is the equivalent draw from a
normal distribution for a standard normal sample variable of 0.67?
A) -13.12
B) 03.12
C) 13.12
D) 23.12
A stock is valued at $28.00. The annual expected return is 9.0% and the standard
deviation of annualized returns is 19.0%. If the stock is lognormally distributed, what is
the price of the stock given a one standard deviation move up after 4 years?
A) $28.00
B) $32.33
C) $40.13
D) $54.60
Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration
and stock price of $72.00. What is the rho of the option as the interest rate changes from
6.0% to 5.0%?
A) 0.07
B) 0.12
C) 0.16
D) 0.20
The prices of 1, 2, 3, and 4-year zero coupon government bonds are 95.42, 90.36,
85.16, and 78.81, respectively. What is the continuously compounded 3-year zero yield?
A) 5.35%
B) 5.85%
C) 6.12%
D) 6.40%
The stock price in KMW, Inc. is $50, $54, $56, and $48 on four consecutive days of
trading. What is the continuously compounded return on the stock over this time frame?
A) -3.85 %
B) -4.00 %
C) -4.08 %
D) -4.16 %
Assume S = $62.50, σ = 0.20, r = 0.03, div = 0.0, on a $60 strike call and 81 days until
expiration. Given a delta = 0.7092, gamma = 0.0582, and theta = -0.0158, what is the
PREDICTED call price, using the delta, gamma, theta approach, after 1 day, assuming a
$0.50 rise in the stock price?
A) $4.364
B) $4.376
C) $4.390
D) $4.392
The pricing of derivatives is linked to the decisions investors make relative to:
A) Black-Scholes variables
B) Money markets
C) Portfolios
D) T-bills
Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar
denominated pound call is $1.30. Assume r = 0.045, rf = 0.06, σ = 0.15 and the option
expires in 180 days. What is the call option price?
A) $0.133
B) $0.143
C) $0.153
D) $0.163
Which distribution is a discrete probability distribution that counts the number of
events, such as large stock price moves, that occur over a period of time?
A) Latin hypercube
B) Normal
C) Lognormal
D) Poisson
The price of a stock is $52.00. Lacking additional information, what is your forecasted
difference between a put option and a call option on this stock? Assume 38 days to
expiration and 6.0% interest.
A) $0.16
B) $0.32
C) $0.48
D) $0.64
Albert, Inc. stock is $42.00 per share. The company’s quarterly dividend is forecasted as
$0.50 per share, increasing 10.0% at the start of every year. What is the price of a
zero-coupon equity-linked bond, promising to pay one share in 3 years, given annual
interest rates of 8.0%?
A) $32.60
B) $36.20
C) $42.60
D) $62.40
The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is
1.40%. The continuously compounded annual interest rate is 8.40%. What is the price
of a forward contract that expires 9 months from today?
A) $937.48
B) $942.66
C) $984.36
D) $1001.69
Zero-coupon bonds maturing in 1, 2, and 3 years have prices of 0.9020, 0.8320, and
0.7620, respectively. What is the implied forward rate from year 2 to year 3?
A) 7.94%
B) 9.19%
C) 09.68%
D) 10.21%
We wish to cap participation in a 3-year equity-linked option at 50.0% return. Our profit
alpha is 3.0%. The S&P 500 price = 950, div = 0.015, σ = 0.22, and interest rates are
4.8%. What is the implied participation rate?
A) 0.66
B) 0.76
C) 0.96
D) 1.16
The current currency spot rate is $1.31 per euro. If dollar denominated interest rates are
3.0% and euro denominated interest rates are 4.0%, what is the likely dollar per euro
exchange rate for a 2-year forward contract?
A) $1.28
B) $1.30
C) $1.31
D) $1.33
A multivariate option that has a claim with a payoff dependent upon the price of two
different assets is known as:
A) Exotics
B) Multioptions
C) Quantos
D) Supershares
Use a binomial tree to value to following option. Assume rf = 0.045, rp = 0.14, σ = 0.20,
E(CF1) = $62 million, g = 0.03, time horizon = 2 years, binomial period = 1 year, and
cost = $500 million. What is the value of this project option?
A) $47 million
B) $57 million
C) $67 million
D) $77 million
To plant and harvest 20,000 bushels of corn, Farmer Jayne incurs fixed and variable
costs totaling $33,000. The current spot price of corn is $1.80 per bushel. What is the
profit or loss if the spot price is $1.90 per bushel when she harvests and sells her corn?
A) $3,000 gain
B) $3,000 loss
C) $5,000 gain
D) $5,000 loss
What does Girsanov’s theorem tell us about drift and Brownian motion?
Why does a company sell a put when issuing compensation options?
Give an example of currency translation that is a change in numeraire.
Instead of issuing a pure commodity-linked debt, why would the commodity producing
firm consider a combining interest plus participation in the commodity price
appreciation?
Give one example of how price discovery functions in the commodity futures market.
What is the recovery rate?
What actions are required to both delta-hedge and gamma-hedge a written option
position?
Explain the process of creating a synthetic Forward Rate Agreement.
Describe briefly the nature of a swap and its primary component.
Why would a corn farmer, who maintains a short futures contract after harvesting and
selling her crop, be considered a speculator?
Why do arbitrage profits rarely exist in interest rate swap pricing?
What purpose do currency linked options serve?
Why is VaR an important tool in measuring risk? What are some of its shortcomings?
How are call and put options used to value starting, stopping, and restarting commodity
extraction projects?
What is the main difference in pricing R & D options versus most other real options?
What advantage does a variance reduction technique offer?
Why is the premium on a standard option and down-and-in call the same when the
barrier price exceeds the stock price?