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. What is
the value of the wager to Joe?
A) $3.00
B) $9.65
C) $12.44
D) $19.58
The value of Z(t) at any point in time can be described as a process in which there is a
cumulative effect of infinitely small movements. This process is called:
A) Ornstein-Uhlenbeck
B) Diffusion
C) Ito
D) Geometric
The difference between the yield to maturity on a defaultable bond and an otherwise
equivalent default-free bind is called the:
A) Credit risk
B) Credit spread
C) Loss given default
D) Recovery rate
In martingale pricing, the observed price of a stock follows a process which substitutes
what variable for alpha?
A) Delta
B) Epsilon
C) Money market rate
D) Risk-free rate
The price of an S&P 500 Index futures contract is $988.26 when you decide to enter a
long position. When the position is closed the futures price is $930.32. If there are no
settlement requirements, what is your percentage gain or loss under a 15.0% margin
requirement? (Ignore opportunity costs.)
A) 39% gain
B) 39% loss
C) 43% gain
D) 43% loss
The price of a 3-year zero coupon government bond is 85.16. The price of a similar
4-year bond is 78.81. What is the 1-year implied forward rate from year 3 to year 4?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
Assume S = $52, K = 50, div = 0.01, r = 0.06, σ = 0.22, and 45 days until expiration.
What is the premium on an Asian average strike call where N = 1?
A) $0.00
B) $0.10
C) $0.20
D) $0.30
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 price of a non-dividend paying stock is $55 per share. A 6-month, at the money call
option is trading for $1.89. If the interest rate is 6.5%, what is the likely price of a
European put at the same strike and expiration?
A) $0.05
B) $0.13
C) $0.56
D) $0.88
A strategy consists of buying a market index product at $830 and longing a put on the
index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per
month, compute the profit or loss from the long put position by itself (in 6 months) if
the market index is $810.
A) $3.45 gain
B) $1.45 gain
C) $2.80 loss
D) $1.36 loss
A firm has a single issue of a zero coupon debt that promises to pay $40 in 5 years, and
the A0 = $50, r = 4%, σ = 12%, and δ = 0. If the asset has a 5% chance of total default,
what is the value of the debt?
A) $30.83
B) $42.68
C) $55.21
D) $62.41
When a stock price movement occurs and is more than we would expect from a
lognormal distribution, we refer to this as:
A) Pull
B) Jump
C) Squat
D) Push
The $850 strike put premium is $25.45 and the $850 strike call is selling for $30.51.
Calculate the breakeven index price for a strategy employing a short call and long put
that expires in 6 months. Interest rates are 0.5% per month.
A) $822.67
B) $824.79
C) $830.76
D) $875.82
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 put on call compound option with an exercise price of $2.00 has
180 days until expiration. What is the premium of the put on call option?
A) $0.42
B) $0.48
C) $0.85
D) $1.11
KidCo bought forward contracts on 20,000 bushels of corn at $1.65 per bushel.
Corporate tax rates are 35.00%. Revenue is $100,000 and other costs are $60,000. Spot
prices on corn are $1.75 per bushel. Calculate the after-tax net income.
A) $7,000 loss
B) $7,000 gain
C) $4,550 loss
D) $4,550 gain
Geek Is Us, Inc. may invest $8 million in an Alien Spectograph project. Annual costs
and revenues, starting next year, are forecasted to be $3 million and $2 million growing
at 0.0% and 4.0%, respectively. If the opportunity cost of capital is 6.0% and σ = 0.0,
what is the investment trigger price?
A) $20.95 million
B) $30.95 million
C) $40.95 million
D) $50.95 million
Will, Inc. stock is $63.35 per share. The company’s quarterly dividend is forecasted as
$0.10 per share, increasing 5.0% every quarter. A coupon equity-linked bond, promising
to pay one share of Will, Inc. in 2 years pays a semi-annual coupon of $0.20. If
annualized interest rates are 8.0%, what is the price of the bond?
A) $59.55
B) $61.14
C) $63.12
D) $65.22
A stock is selling for $68.50. Interest rates are 6.0% and the returns on the stock have a
standard deviation of 32.0%. What is the forecasted price of the stock using 3-month
periods at Suudu?
A) $74.08
B) $94.24
C) $100.17
D) $111.12
Your portfolio is worth $200,000. The standard deviation of its annual returns is 0.20
and the expected return is 11.0%. What is the 2-week value at risk at a 95% confidence
level?
A) $12,058
B) $13,058
C) $14,058
D) $15,058
What type of random variable is necessary for a Monte Carlo valuation?
A) Standard normal distribution
B) Normal distribution
C) Lognormal distribution
D) All of the above
Which of the following options would not benefit from using a Monte Carlo
simulation?
A) American
B) Asian
C) European
D) Barrier
A stock is selling for $32.70. The strike price on a call, maturing in 6 months, is $35.
The possible stock prices at the end of 6 months are $39.50 and $28.40. If interest rates
are 6.0%, what is the option price?
A) $1.90
B) $2.80
C) $3.40
D) $4.20
A firm provides a service that benefits from decreasing employment. This firm has a
risk exposure to macro event. All other variables being equal, which of the following
derivative securities is the firm most likely use to hedge its exposure?
A) Short position in an economic futures
B) Long position in an economic futures
C) Short position in an interest rate futures
D) Long position in an interest rate futures
Given a mean of 4.5 and a standard deviation of 12 from a sample of variables, what is
the equivalent draw from a standard normal distribution for 6.0?
A) 0.065
B) 0.075
C) 0.095
D) 0.125
The negative correlation between stock prices and volatility is referred to as the:
A) Correlation effect
B) Correlation risk
C) Leverage effect
D) Leverage risk
Consider a one-period binomial model of 12 months. Assume the stock price is $54.00,
σ = 0.25, r = 0.04 and the exercise price of a call option is $55. What is the forecasted
price of the stock given an upward movement during the year?
A) $56.16
B) $61.01
C) $65.12
D) $72.16
Which of the following is NOT a source of cash while maintaining a delta neutral
hedge?
A) Borrowing
B) Purchase or sale of shares
C) Interest
D) Self financing
Assume S = $52.50, K = $55, σ = 0.20, r = 0.045, T – t = 130 days, div = 0.01, and a
jump probability = 0.007. What is the value of a put option?
A) $3.63
B) $2.63
C) $1.63
D) $0.63
The S&P 100 Index implied volatility since 2003 is published by the CBOE under the
ticker symbol:
A) IVX
B) SP1X
C) VIX
D) VXO
Monte Carlo simulation assumes all assets earn:
A) Risk-free rate
B) Market Index return
C) YTM on AAA Bonds
D) Brokers call
What is a credit default swap and what function does it serve?
Explain the relationship between strike prices and implied volatilities under a price
jump scenario.
Under what circumstances would a multinational company elect to enter into a currency
swap agreement?
Under what conditions does delta-gamma-theta approximate the exact bond price
change?
Why are exotic options not so exotic?
In the context of peak-load energy generation and a European exchange option, what is
the spark spread?
Provide a definition of Brownian motion.
Why are synthetics created and/or calculated when the actual derivative is available?
How does a dividend payment impact the option price?
Why might the manager of a portfolio employ a protective put strategy?
For whom would the issue of an oil-linked debt instrument not be considered a risky
issue?
What are the various models in bond pricing and behavior?
For families employed and living in “company towns” (i.e., where the major employer
owns all homes, retail stores, etc.), explain the lack of diversification.
Using a binomial tree explanation, explain the situation in which an American option
would alter the pricing of an option.
Explain how a negative correlation between agricultural production and commodity
prices creates a natural hedge.