Assume the spot price of gold is $745 per ounce and the 2-year forward price is $773.
Annualized 1-year and 2-year forward interest rates are 5.0% and 5.2%, respectively.
For a commodity-linked note to sell at par, what is the annual coupon?
A) $23.09
B) $24.09
C) $25.09
D) $26.09
Given a mean of -7.8 and a standard deviation of 16 from a normally distributed
sample, what is the probability of an observation being below 12.0?
A) 0.51
B) 0.61
C) 0.71
D) 0.81
If next year’s bond prices for 2-year zero coupon bonds may be either 0.9454 or 0.9233,
what is the yield volatility?
A) 18%
B) 16%
C) 14%
D) 12%
Nine-month gold futures are trading for $1565 per ounce. The spot price is $1509 per
ounce. LIBOR during each of the upcoming 4 quarters is listed as 1.04%, 1.22%,
1.30%, and 1.35%, respectively. Calculate the 9-month lease rate on the futures
contract.
A) 2.4%
B) 2.1%
C) 1.3%
D) 0.0%
Assume that a $55 strike call has a 1.5% continuous dividend, r = 0.05 and the stock
price is $50.00. If the option has 45 days until expiration, what is the vega, given a shift
in volatility from 33.0% to 34.0%?
A) 0.20
B) 0.15
C) 0.10
D) 0.05
Assume that a $60 strike call pays a 1.0% continuous dividend, r = 0.05, σ = 0.28, and
the stock price is $62.00. What is the profit or loss per share if on a long call position,
with 73 days until expiration, the price immediately rises to $63.00?
A) $0.68 gain
B) $0.68 loss
C) $0.88 gain
D) $0.88 loss
A stock price has a historical volatility of 24%. If an anomalous event occurs to the
company in the next past two days, which was not anticipated, what is the most likely
implied estimate of the unconditional volatility using the GARCH model?
A) 12%
B) 20%
C) 27%
D) 45%
Use a binomial tree to value the following option. Assume rf = 0.04, rp =0.12, σ = 0.35,
E(CF1) = $30, and cost = $300. What is the value of this project option?
A) $40.74
B) $50.60
C) $55.32
D) $62.12
Assume a = 0.10, b = 0.15, r = 0.04 and σ = 0.35. Using the CIR model, calculate the
price of a zero coupon bond maturing in 6 years.
A) 0.6042
B) 0.7042
C) 0.8042
D) 0.9042
Bonds maturing in 1, 2, and 3 years have prices of 0.9020, 0.8320, and 0.7620,
respectively. What is the price of a put option that expires in 1 year that gives you the
right to sell a 1-year bond for a price of 0.9200? Assume σ = 0.18.
A) $0.35
B) $0.25
C) $0.15
D) $0.05
What do we call an option in which the holder has a claim that pays one share of stock
if
S(T) > K, and nothing otherwise?
A) Cash-or-nothing option
B) Asset-or-nothing option
C) Exotic option
D) Digital cash
The current price per ton of iron ore is $145.00. The effective lease rate is 3.0% and the
risk free rate is 4.5%. The cost to mine one ton of iron ore is $110.00 and constant.
What is the trigger price at which we will mine the iron ore?
A) $163.80
B) $180.40
C) $210.50
D) $205.70
What is net dollar gain or cost required to create a short put delta hedge against a 100
short put position? Assume puts are priced at $1.98, the delta is 0.489, the stock price is
$34.50, and no cost to short stock.
A) $1,540.50 gain
B) $1,540.50 cost
C) $2,319.58 gain
D) $2,319.58 cost
Assume the net swap payment is $.50 on a reverse transaction involving a 3-year oat
swap. What is the market value of the swap given interest rates on zero coupon treasury
bonds are 5.2%, 5.6%, and 6.0% for 1, 2, and 3 years, respectively?
A) $0.96
B) $1.10
C) $1.25
D) $1.34
Consider a two-period binomial model, where each period is 6 months. Assume the
stock price is $46.00, σ = 0.28, r = 0.06 and the dividend yield is 2.0%. What is the
maximum approximate strike price where early exercise would occur with an American
call option?
A) $29
B) $33
C) $42
D) $46
Compute the yield on debt given a 10-year zero-coupon bond paying $500 at maturity.
Assume the asset value is $450, σ = 0.35, r = 0.06, and no dividend is paid.
A) 6.62%
B) 7.26%
C) 8.26%
D) 9.62%
The annualized dividend yield on the S&P 500 Index is 1.40%. The continuously
compounded interest rate is 6.4%. If the 9-month forward price is $925.28 and the
index is priced at $950.46, what is the profit/loss from a cash-and-carry strategy?
A) $25.18 loss
B) $25.18 gain
C) $61.50 loss
D) $61.50 gain
The current Nikkei index price is 21,200. Assume σ = 0.13, r = 0.05 and div = 0.015. If
K = 20,000 yen and yen per dollar spot rates are 103, what is the dollar value of a
2-year call?
A) $13.97
B) $18.97
C) $23.97
D) $28.97
Harold owns 10,000 shares of IBM at $54.50 per share. He writes $55 strike covered
call on all the shares. Assume = 0.14, σ = 0.18, rf = 0.04, and the options expire in 90
days. What is the value at risk for 1 day, using the delta approximation at a 95%
confidence level?
A) $4,717
B) $5,717
C) $6,717
D) $7,717
Consider a two-period binomial model, where each period is 6 months. Assume the
stock price is $60.00, σ = 0.30, r = 0.05. An American put option with a strike price of
$65 would be exercised early at what dividend yield?
A) 5.0%
B) 6.0%
C) 11.0%
D) Never exercised early
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 is paid one share of ABC Corp. stock if the price is below $85.00. What is
the value of her wager?
A) $21.80
B) $22.80
C) $23.80
D) $24.80
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 implied 2-year forward rate between years 2
and 4?
A) 4.8%
B) 5.2%
C) 5.5%
D) 6.4%
Suppose the 120-day futures price on crude oil is $115.00 per barrel and the volatility is
20.0%. Assume interest rates are 3.5%. What is the price of a $110 strike call futures
option that expires in 120 days?
A) $3.09
B) $2.99
C) $2.89
D) $2.79
The 6-month futures price for oil is $96.60 per barrel (or 2.30 cents per gallon). The
6-month futures prices for gasoline and heating oil are 2.50 cents and 2.15 cents,
respectively. What is the gross margin on a simple 3-2-1 crack spread?
A) $0.25
B) $0.35
C) $0.54
D) $0.68
Bonds maturing in 1, 2, and 3 years have prices of 0.9345, 0.8766, and 0.8212,
respectively. What is the price of a call option that expires in two years and gives you
the right to pay 0.8600 to buy the 1-year bond? Assume σ = 0.15.
A) $0.015
B) $0.105
C) $0.205
D) $0.305
Using a binomial tree, what is the price of a $40 strike 6-month call option, using
3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%,
σ = 0.35
A) $2.50
B) $2.76
C) $2.92
D) $3.08
The Nikkei index is 22,550, K = 21,000, σ = 0.19, rf = 0.04, S = 0.10, r = 0.08 and
div = 0.01. The yen to dollar spot rate is 104 and the correlation coefficient is 0.30.
What would be the dollar price of a 2-year equity-linked foreign exchange call?
A) $45.02
B) $35.02
C) $25.01
D) $15.02
For a utility function that exhibits decreasing martingale utility, the martingale utility is
low when:
A) Consumption and utility are low
B) Consumption and utility are high
C) Consumption is low and utility is high
D) Consumption is high and utility is low
The spot price of the market index is $900. After 3 months, the market index is priced at
$920. An investor has a long call option on the index at a strike price of $930. After 3
months, what is the investor’s profit or loss?
A) $10 loss
B) $0
C) $10 gain
D) $20 gain
A bond has a current value of $950 and promises to pay $1,000 at the end of 4 years.
The expected return on the asset is 12% and the risk free rate is 3%. If the actual cash
payout in case of default is 0, what is the true default probability given that the asset has
a standard deviation of 18%?
A) 15.2%
B) 21.5%
C) 33.2%
D) 49.6%
Assume that you open a 100-share short position in Jiffy, Inc. common stock at the
bid-ask prices of $32.00 – $32.50. When you close your position, the bid-ask prices are
$32.50 – $33.00. You pay a commission rate of 0.5%. The market interest rate is 5.0%
and the short rebate rate is 3.0%. What is your additional gain or loss due to leasing the
asset?
A) $64.00 loss
B) $160.00 loss
C) $96.00 gain
D) $0
When selecting among various put options with different strike prices, in order to hedge
a long asset position, which of the following statements is true?
A) Higher strike puts cost more and provide higher floors
B) Higher strike puts cost less and provide higher floors
C) Lower strike puts cost more and provide higher floors
D) Lower strike puts cost less and provide higher floors
What is the boundary condition for a European put option?
A) Max [0,S(T)-K]
B) Max [0,K-S(T)]
C) Min [0,S(T)-K]
D) Min [0,K-S(T)]
In the case of a European Outperformance Option, we assume the strike asset is:
A) Cash
B) A money market fund
C) A stock or an index
D) A zero-coupon bond
The S&P 100 Index implied volatility prior to 2003 is published by the CBOE under the
ticker symbol:
A) IVX
B) SP1X
C) VIX
D) VXO
Why is the cash-and-carry strategy employed in the financial futures market not readily
available in the commodity futures market?
Explain the steps necessary to take advantage of an arbitrage opportunity, which may
exist between the dollar and yen, when a future yen payment is required.
The equation used by Black and Scholes to characterize the behavior of an option,
expressed with Greeks, holds true for American options as well as European options
with one exception. What is the exception?
How does the number of draws impact the validity of a Monte Carlo simulation?
What function does the convenience yield serve in setting forward prices and how does
this influence arbitrage opportunities?
How does the node configuration in interest rates and bonds differ from stocks?
The necessary condition for early exercise is that we prefer to receive something sooner
rather than later. With a dividend paying call and a non-dividend paying put, what do
we receive?
How do asset values differ between using a traditional DCF approach and a stochastic
discount factor approach?
What is the relationship, in general, between volatility and trigger prices, assuming
constant costs?
An investor has a long call option on the market index at a strike price of $930. At
expiration the index price is $920. Explain the profit and loss.
What is the difference between naked and covered call writing?
Explain how a long stock and long put strategy equals the cash flow from a long call
strategy.
What is the relationship of the Sharpe ratios and risk premiums between stocks and
options?
What is the primary potential for error when using the Cox-Ross-Rubenstein binomial
tree?
The use of collars in acquisitions serves the purpose of addressing what two issues in an
offer?