What is the maximum profit that an investor can obtain from a strategy employing a
long 830 call and a short 850 call over 6 months? Interest rates are 0.5% per month.
A) $6.80
B) $7.68
C) $9.24
D) $12.32
A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.
If settled in arrears, what amount would the borrower pay or receive on an $800,000
loan if the prevailing 6-month interest rate is 3.6%?
A) $4,000 payment
B) $4,000 receipt
C) $1,729 payment
D) $1,729 receipt
What technique might be used to improve the accuracy of a Monte Carlo simulated
output?
A) Arithmetic Asian option
B) Control variate method
C) Poisson Distribution with jumps
D) Risk neutral probabilities
Assume oat forward prices over the next 3 years are $2.25, $2.35, and $2.28,
respectively. Effective annual interest rates over the same period are 5.2%, 5.5%, and
5.8%. What is the
2-year swap price on a hypothetical “forward swap” that begins at the end of year 1?
A) $2.14
B) $2.32
C) $2.41
D) $2.53
Farmer Jayne decides to hedge 10,000 bushels of corn by purchasing put options with a
strike price of $1.80. Six-month interest rates are 4.0% and the total premium on all
puts is $1,200. If her total costs are $1.65 per bushel, what is her marginal change in
profits if the spot price of corn drops from $1.80 to $1.75 by the time she sells her crop
in 6 months?
A) $248 loss
B) $0
C) $252 gain
D) $1,500 loss
An investor enters into a 2-year swap agreement to euros at $1.32 per euro. Soon after
the swap is created forward prices rise and the new swap price on a similar swap is
$1.45. If dollar denominated interest rates are 4.0% and 4.5% on 1- and 2-year zero
coupon government bonds, respectively, what is the gain to be made from unwrapping
the original swap agreement?
A) $0.24
B) $0.45
C) $0.65
D) $0.82
Compute the conversion factor on a semi-annual 6.8% coupon bond, which matures in
exactly 5 years.
A) 1.037
B) 1.046
C) 1.052
D) 1.068
Cyril is purchasing a down-and-in cash call. H = $45.00, S = $38.24, K = $35, σ = 0.33,
r = 0.05, div = 0 and it expires in 140 days. What is the value of the option if the
payment is $1.00?
A) $0.80
B) $1.80
C) $2.80
D) $3.80
Kelly owns 50,000 shares of Microsoft at $63.60 per share. She buys 20,000 $60 strike
calls. Assume = 0.12, σ = 0.23, rf = 0.05, and the options expire in 170 days. What is
the value at risk for 2 weeks, using the delta approximation at a 99% confidence level?
A) $311,463
B) $411,463
C) $511,463
D) $611,463
Assume S = $55, K = $55, r = 0.07, σ = 0.27, div = 0.0, and 180 days until expiration.
What is the premium on an Asian average price call, where N = 5?
A) $2.89
B) $2.99
C) $3.09
D) $3.19
The spot price of the market index is $900. After 3 months the market index is priced at
$915. The annual rate of interest on treasuries is 2.4% (0.2% per month). The premium
on the long put, with an exercise price of $930, is $8.00. Calculate the profit or loss to
the short put position if the final index price is $915.
A) $15.00 gain
B) $15.00 loss
C) $6.95 gain
D) $6.95 loss
What is the 3-year swap price on corn? Assume interest rates over the next 3 years are
2.0%, 2.5%, and 2.8%. The prepaid swap price is given as $15.50.
A) $5.10
B) $5.30
C) $5.43
D) $5.64
The spot price of corn is $5.85 per bushel. The opportunity cost of capital for an
investor is 0.5% per month. If storage costs of $0.04 per bushel per month are factored
in, all else being equal, what is the likely price of a 4-month forward contract?
A) $5.808
B) $5.736
C) $5.968
D) $6.006
The case where the zero coupon bond is selected as the numeraire under a risky asset
method results in a measure called the:
A) Drift measure
B) Forward measure
C) Money market measure
D) Spread measure
The value of an Asian put option is computed using the geometric average strike. What
is the expected payoff if the observed prices to date are 71, 72, 70, 68, 69, and 68,
respectively?
A) 1.35
B) 1.45
C) 1.55
D) 1.65
Your $2 million portfolio consists of 25% Evans stock with = 0.16, σ = 0.22 and 75%
Indy stock with = 0.09, σ = 0.12. The correlation coefficient is 0.13. What is the
value at risk over 1 day at a 99% confidence level? Assume 252 days per year.
A) $21,792
B) $31,792
C) $41,792
D) $51,792
The premium on a call option on the market index with an exercise price of 1050 is
$9.30 when originally purchased. After 2 months the position is closed, and the index
spot price is 1072. If interest rates are 0.5% per month, what is the Call Profit?
A) $9.30
B) $9.39
C) $12.61
D) $22.00
Assume S = $51, K = $50, div = 0.0, r = 0.05, σ = 0.20, and 55 days until expiration.
What is the premium on a knock-in call option with a down-and-in barrier of $48?
A) $0.175
B) $0.185
C) $0.195
D) $0.205
Assume S = $53, K = 50, div = 0, r = 0.03, σ = 0.30, and 100 days until expiration.
What is the premium on a knock-in put option with an up-and-in barrier of $55?
A) $0.63
B) $0.73
C) $0.83
D) $0.93
If your homeowner’s insurance premium is $1,000 and your deductible is $2000, what
could be considered the strike price of the policy if the home has a value of $120,000?
A) $118,000
B) $120,000
C) $117,000
D) $122,000
The manager of a blue chip growth stock mutual fund is trying to fully hedge the $650
million portfolio position during the last two months of the calendar year. The current
price of the S&P 500 Index futures contract is 1200. If the mutual fund has a beta of
1.24, how many contracts will be needed to hedge the fund?
A) 1,083
B) 3,033
C) 242,963
D) 541,666
Assume a = 0.15, b = 0.08, r = 0.05, and 0.30. Using the CIR model, calculate the delta
of a zero coupon bond maturing in 5 years.
A) -4.08
B) -3.08
C) -2.08
D) -1.08
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 dollar gain or loss? (Ignore opportunity costs.)
A) $14,485 loss
B) $14,485 gain
C) $57.94 loss
D) $57.94 gain
The S&P 500 Index is priced at $950.46. The annualized dividend yield on the index is
1.40%. What is the price of a 6-month prepaid forward contract on the S&P 500 Index?
A) $943.83
B) $950.00
C) $964.26
D) $984.21
Wayne, Inc. stock is $40.00 per share. The company’s quarterly dividend is forecasted
as $0.45 per share, indefinitely. A coupon equity-linked bond, promising to pay one
share of Wayne, Inc. in 3 years pays a quarterly coupon of $0.50. If annual interest rates
are 4.0%, what is the price of the bond?
A) $40.56
B) $42.60
C) $44.56
D) $46.60
The value of an Asian call option is computed using the geometric average strike. What
is the expected payoff if the observed prices to date are 69, 70, 72, 71, 75, and 73,
respectively?
A) 1.26
B) 1.36
C) 1.46
D) 1.56
Compute Δ for the following call option. The stock is selling for $23.50. The strike
price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75.
A) 0.4091
B) 0.6822
C) 0.8433
D) 0.9216
Interest rates on the U.S. dollar are 5.4% and euro rates are 4.6%. Given a dollar per
euro spot rate of 0.918, what is the 6-month forward rate ($/E)?
A) 0.912
B) 0.917
C) 0.922
D) 0.934
If an investor is speculating with a long call position, what is the most likely preference
of the investor, relative to a change in rho?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
A firm has a single issue of a zero coupon debt that promises to pay $90 in 4 years, and
the A0 = $100, r = 4%, σ = 25%, and δ = 0. If the asset has a 2% chance of total default,
what is the value of the debt?
A) $67.10
B) $75.19
C) $85.62
D) $90.00
From a strictly conceptual perspective, why would any manufacturer consider hedging
their variable costs? Answer as if you own the company.
What is the characteristic that makes options, like quantos, multivariate options?
Why is recent data more relevant than older data when calculating volatility?
Give a very brief definition of conditional expected stock price.
In a lognormal model of stock price movement, describe the mean and variance of the
continuously compounded returns.
Why are managerial controls over option and forward trading departments vital to
proper risk control?
Engage the class in a conversation about auto insurance. Why do people feel their
premium is wasted if they do not file a claim?
Explain the impact a constant dividend yield would have on the price of a call option.
What prevents a market-maker from readjusting her delta hedge on a continual basis?
What is bootstrapping and what is its use?
What unique feature about perpetual options makes it possible to derive a valuation
formula?
How does a control variate method make a naive Monte Carlo more efficient?
What two components go into valuing an infinite commodity reserve?
What is the transaction that results within an interest rate cap to make the holder’s rate
“capped”?
Why are covariances and correlations relevant to simulation development?
What are the two methods by which insurance companies hedge their risk of extreme
losses?
What is a default swap and what is its use?
How are partial expectation prices converted to conditional expectation prices?