A stock has a historical volatility of 39%. The data shows significantly increased
volatility in recent data and significantly lower volatility in older data. The implied
estimate of the unconditional volatility using the GARCH model is most likely to be
which of the following?
A) 12%
B) 25%
C) 45%
D) 85%
Consider an investment in five S&P 500 Index futures contracts at a price of $924.80.
The initial margin requirement is 15.0% and the maintenance margin is 10.0%. If the
continuously compounded interest rate is 5.0% what will the futures price need to be for
a margin call to occur 10 days from now? Assume no settlement within the 10 days.
A) $852.64
B) $872.79
C) $898.63
D) $905.25
If using Monte Carlo simulation, what is a typical number of iterations employed in the
model?
A) 1
B) 10
C) 1,000
D) 1,000,000
Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The
spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are,
101.51, 99.08, 96.71, and 94.40, respectively. What is the present value of the
market-maker’s net cash flow if spot rates are 102 instead?
A) $188.59
B) $206.43
C) $219.96
D) $242.06
Assume the following: LN(S) and LN(Q) have a correlation coefficient of -0.65, S(0) =
55, Q(0) = 60, r = 0.04, σs = 0.22 σQ = 0.15, and dividends = 0. Using formula 20.39,
what is the price of a claim that pays Q/ ?
A) $8.16
B) $9.16
C) $10.16
D) $11.16
A commodity linked bond is issued with an embedded call option. The current
commodity price is $110, as is the exercise price on the call option. The call option is
priced at $3.41. If the promised payment on the bond is the same as the issue price of
$100, what is the implied coupon if effective interest rates are 3.0% and the bond has a
1-year maturity?
A) $0.66
B) $0.77
C) $0.88
D) $0.99
What economic concept is central to proving that risk neutral pricing functions in the
establishing of option prices?
A) Consumption possibilities
B) Factor analysis
C) Marginal average cost
D) Declining marginal utility
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 probability of a loss over 10 business
days?
A) 39.84%
B) 49.84%
C) 59.84%
D) 69.84%
Rankin Corp. common stock is priced at $74.20 per share. The company just paid its
$1.10 quarterly dividend. Interest rates are 6.0%. A $70.00 strike European call,
maturing in 6 months, sells for $6.50. How much arbitrage profit/loss is made by
shorting the European call, which is priced at $2.50?
A) $0.12 loss
B) $0.12 gain
C) $0.36 loss
D) $0.36 gain
Assume the following: LN(S) and LN(Q) have a correlation coefficient of 0.40, S(0) =
60, Q(0) = 60, r = 0.05, σs = 0.30 σQ = 0.25, and dividend = 0. Using formula 20.39,
what is the price of a claim that pays ?
A) $243.96
B) $322.96
C) $479.96
D) $532.96
Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01, on a $35 strike call. Given delta =
0.3854 and gamma = 0.0847, what is the delta-gamma approximation for the call price
on a $0.50 stock price increase? Assume 68 days until expiration.
A) $1.34
B) $1.36
C) $1.38
D) $1.40
Mel, Inc. stock is $135.00 per share. The company’s semi-annual dividend is forecasted
as $2.10 per share, indefinitely. What is the price of a zero-coupon equity-linked bond,
promising to pay one share in 3 years, given annual interest rates of 5.0%?
A) $101.35
B) $110.26
C) $123.45
D) $155.22
Assume that a $50 strike call has a 3.0% continuous dividend, σ = 0.27, r = 0.06 and 60
days from expiration. What is the gamma for a stock price movement from $48.00 to
$49.00?
A) 0.046
B) 0.074
C) 0.089
D) 0.099
Consider the case of an exchange option in which the underlying stock is Eli Lilly and
Company with a current price of $56.00 per share. The strike asset is Merck, with a per
share price of $52.00. Interest rates are 5% and the 3-month call option is trading for
$7.00. What is the price of the put?
A) $3.00
B) $4.00
C) $7.00
D) $11.00
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
feature?
A) $2.25
B) $3.29
C) $4.11
D) $4.78
An investor enters into a 2-year swap agreement to purchase crude oil at $105.65 per
barrel. Soon after the swap is created forward prices rise and the new swap price on a
similar swap is $108.32. If interest rates are 3.0% per year, what is the gain to be made
from unwrapping the original swap agreement?
A) $2.67
B) $5.11
C) $5.34
D) $5.67
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. If the price is below $85.00, Pat must pay $5.00. What is the net value of Pat’s
wager?
A) -$2.49
B) +$2.49
C) -$1.50
D) +$1.50
Which of the following options will NOT be exercised early?
A) Put on a dividend paying stock
B) Call on a dividend paying stock
C) Put on a non-dividend paying stock
D) Call on a non-dividend paying stock
Assume the spot price of gold is $750 per ounce, the 1-year forward price is $770, and
the annual interest rate is 4.5%. What is the price of a zero-coupon note paying 1 ounce
of gold in one year?
A) $770
B) $750
C) $725
D) $736
A stock is selling for $18.50. The strike price on a call, maturing in 6 months, is $20.
The possible stock prices at the end of 6 months are $22.50 and $15.00. Interest rates
are 6.0%. How much money would you borrow to create an arbitrage on a call trading
for $2.00?
A) $2.54
B) $4.85
C) $6.60
D) $8.85
Since delta of an option changes over the same time period that a stock price is
changing, what is the delta used to calculate the approximate change in the option
price?
A) Delta at the start of the time period
B) Delta at the end of the time period
C) The average delta over the time period
D) The median delta over the time period
HAW, Inc. plans to pay a $1.10 dividend per share in 3 months and a $1.15 dividend in
6 months. HAW’s share price today is $45.60 and the continuously compounded
quarterly interest rate is 2.1%. What is the price of a forward contract, which expires
immediately after the second dividend?
A) $45.28
B) $45.96
C) $45.60
D) $46.24
The price of a bond that matures in 1 year is 103.34, using base 100 pricing. The price
of a bond that matures in two years is 101.90, using base 100 pricing. What is the
1-year bond forward price in year 1?
A) 98.56
B) 98.61
C) 101.90
D) 103.34
Assume the price of Mary, Inc. stock is $56.00, interest rates are 4.8%, div yield = 0,
and
σ = 0.35. What is the price of a $1,000 par value 2-year price-participation note paying
a 5.0% annual coupon and receiving 50.0% of all price appreciation above $65.00?
A) $896.44
B) $996.44
C) $1006.44
D) $1106.44
Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The
spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are,
101.51, 99.08, 96.71, and 94.40, respectively. What is the dollar value of a 4-year 1
million yen loan?
A) $9,615.33
B) $10,422.46
C) $11,618.04
D) $13,527.89
The spot price of the market index is $900. After 3 months the market index is priced at
$920. 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. What is the profit or loss at
expiration for the long put?
A) $2.00 gain
B) $2.00 loss
C) $1.95 gain
D) $1.95 loss
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 par coupon on a 4-year coupon bond selling
at par?
A) 5.02%
B) 5.43%
C) 5.81%
D) 6.06%
During the growing season, a corn farmer sells short corn futures contracts in an
amount equal to her crop. If upon harvesting and selling her crop she maintains the
contracts, she is then considered a(n):
A) Hedger
B) Speculator
C) Arbitrager
D) None of the above
Albert has accepted a wager to receive $5.00 if the price of Will Co. is above $35.00 per
share. This right only exists if Will Co. drops below $33.00 sometime over the coming
100 days. Currently, Will Co. stock price is $38.24, r = 0.05, σ = 0.33, and div = 0.
What is the value of Albert’s position?
A) $0.35
B) $0.25
C) $0.15
D) $0.05
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 risk neutral default probability?
A) $369
B) $400
C) $470
D) $500
The process of moving from one probability distribution to another is called:
A) Brownian motion
B) Change of measure
C) Stochastic discount factor
D) Utility function
A forward contract that pays the difference between a forward price and some measure
of the realized stock variance is called a Variance:
A) Skew
B) Smile
C) Surface
D) Swap
When considering drift and noise, how would you explain price movements over
smaller and smaller time intervals?
What are two important implications of assuming that prices follow a geometric
Brownian motion?
How does the Black-Scholes equation explain the pricing of derivatives?
Under what circumstances should an option be exercised early?
Why would an exponentially weighted moving average be a more accurate means of
calculating volatility than a simple sampling of historical data?
Explain the expectations hypothesis and its ability to accurately forecast interest rates.
What three components exist in the value of an “outperform stock option”?
What is the difference between a standard bull spread and a calendar bull spread?
Define the term drift.
Using the synthetic long stock strategy, explain the difference in call and put prices.
What is the primary difference between a standard option and an exchange option?
Define a power option.