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For each problem, choose the answer choice that best answers the question.
The continuously-compounded zero rate for a bond with maturity in 0.5 years is 3.3%. The continouslycompounded zero rate for a bond with maturity in 1 year is 3.6%. The continuously compounded forward
rate for a loan to be made in 0.5 years and paid back in 1.5 years (1 year after the loan is made) is 3.9%.
What is the price of a zero-coupon bond with face value of $100 maturing in 1.5 years?
I have created a bear spread by buying a put option with a strike price of $25 and selling a put option with
a strike price of $20. If the price of the underlying stock at expiration is $23.50, what is the payoff of my
Which of the following statements regarding option Greeks is FALSE?
1) Holding all else equal, the vega of an at-the-money option is higher than the vega of an outof-the-money option or the vega of an in-the-money option.
2) Holding all else equal, the theta of an at-the-money option is much smaller in magnitude
than the theta of an out-of-the-money or in-the-money option.
3) The gamma of all options is positive.
4) Holding all else equal, the gamma of an at-the-money option is higher than the gamma of an
out-of-the-money option or the gamma of an in-the-money option.
Which of the following is FALSE regarding the Black-Scholes-Merton option
1) If N(d 1 ) is between -1 and 1 then N(d 2 ) will be greater than 1
in absolute value, and vice versa.
2) As the spot price of the underlying stock gets very high, d 1 gets
very large and N(d 1 ) approaches 1.00.
3) N(d 2 ) is the risk-neutral probability that a call option will be
4) As the spot price of the underlying stock gets very small
(approaches 0), d 1 becomes negative and large in magnitude
and N(d 1 ) approaches 0.
You own a 2-month European put option with a strike price of $30 on a stock that is currently worth $35. The
implied volatility of the option you own is 20%. News on the stock is announced that causes investors to be
unsure about the future prospects of the firm. In a very short amount of time the price of the stock drops to
$28 and the volatility used to price the option jumps to 24%. Which of the following is true regarding the value
of the put option?
The value of the put option decreases.
The value of the put option may increase but it also may decrease.
The value of the put option increases.
The value of the put option stays the same.
On June 18th, an investor took a short position in 8 September wheat futures contracts when the futures
price was $5.36. Each contract is on 5,000 bushels of wheat. The initial margin is $1,430 per contract and
the maintenance margin is $1,300 per contract. On July 22nd, the investor gets a margin call requiring an
additional deposit of $2,000. On August 13th, the investor buys back all 8 futures contracts when the
futures price is $5.48. How much money did the investor make or lose on the futures trade?
Gain of $3,370
Gain of $600
Loss of $4,800
Loss of $3,370
According to the Black, Scholes, Merton option pricing model, what is the value of a 6-month European
call option with a strike price of $21 on a stock that is worth $19 today, pays no dividends, and has a
volatilty of 45%? The risk-free rate is 5%. When answering this question you may use the information
The current S&P 500 index level is 2,106. The 6-month continuously compounded zero rate is 4%.
The 6-month forward price for the S&P 500 index is 2128.23. What is the dividend yield on the S&P
The current price of a stock is $20. If I believe that over the next 3 months the price of a
stock is going to stay very close to $20, which of the following option strategies could I use to
create a portfolio that will profit if my prediction is correct?
Long brass monkey
Long butterfly spread
I own a 3-month straddle position comprised of European options with a strike price of $42 on a non-dividendpaying stock with market price of $45. The risk-free rate is 2% and the price of the put position in my straddle is
$4.31. What is the total price of my straddle position?
Which of the following regarding cross-hedging with futures contracts is TRUE?
1) When choosing which futures contract to use as the hedge, the best contract
to use is the contract that has the lowest volatility because this is the least
2) When choosing which futures contract to use as the hedge, the best contract
to use is the contract that has the lowest hedge ratio.
3) When choosing which futures contract to use as the hedge, the best contract
to use is the contract that has the highest correlation with the asset being
4) When choosing which futures contract to use as the hedge, the best contract
to use is the contract that has the highest hedge ratio.
Ten years ago I took a 30-year loan at a fixed interest rate of 5% per year. Now, I want to transform the
loan from a fixed rate loan into a floating rate loan. Which of the following will achieve my objective?
1) Enter an interest rate swap in which I will receive a fixed rate of interest and pay a floating
rate of interest.
2) Enter an interest rate swap in which I will receive a floating rate of interest and pay a fixed
rate of interest.
3) Buy a fixed rate bond.
4) Buy a floating rate bond.
My business will sell machinery to a foreign firm for 25 million euros in September. The current exchange
rate for euros is $1.18 per euro. I want to take an option position that locks in a minimum effective
exchange rate of $1.15 per euro in September. Which of the following positions is most appropriate?
Long position in September euro puts with a strike of $1.15
Short position in September euro puts with a strike of $1.15
Short position in September euro calls with a strike of $1.15
Long position in September euro calls with a strike of $1.15
You are using a 1-step binomial tree to price a derivative security whose payoff is
determined by the price of XYZ stock in 1 month. XYZ stock pays no dividends. The price of
XYZ stock in 1 month will be either $83.50 or $77.25. If the price of XYZ stock in 1 month is
$83.50, the payoff of the derivative contract will be $5.25. If the price of XYZ stock in 1
month is $77.25, the payoff of the derivative contract will be $10.25. What position in XYZ
stock, combined with a LONG position of 1 derivative contract, will produce a riskless
Long 0.8 shares
Short 1.25 shares
Short 5 shares
Long 1.25 shares
You have purchased 3 call options with a strike price of $40 for a price of $11.99 each. You also sold 2 put
options with a strike price of $45 for a price of $2.94. Finally, you sold 6 call options with a strike price of $50
for a price of $5.96. All of the options are European options with the same underlying security and same
expiration date. On the expiration date, the price of the undelrying stock is $43.50. What is the payoff you
receive from your portfolio?
The table below gives the implied volatilities of European options on a stock with strike
price of $30 and expirations ranging from 1 month to 6 months. What would be the most
reasonable implied volatility to use to price a put option with a strike price of $30 that has 2
months until expiration?
Time to Expiration
The 2-year zero rate is 2.8%. The forward rate for a deposit to be made in 6 months and paid back in 2
years (1.5 years after the deposit is made) is 2.5%. What is the 6-month zero rate? All rates in this
problem are continuously compounded rates.
You own a portfolio of European options on non-dividend-paying stocks with a total
theta of -1,212,939 (theta is calculated as a rate per year). If, in one day, the prices
and volatilities of all stocks underlying the options in your portfolio are the same as
they are today, and the risk-free rate has not changed, what is the approximate profit
or loss you will earn on your portfolio? Positive values represent a gain and negative
values represent a loss. When answering this question you should consider the
passage of time with respect to the number of trading days (not calendar days) per
I own a bond portfolio that consists of 2 different bond positions. I own $22 million worth of
bond A, which has a duration of 12.4 years. I own $18 million of bond B, which has a duration of
8.9 years. If the yield on my portfolio increases by 0.08%, approximately how much will the
value of my bond portfolio change?
The price of a non-dividend paying stock is $53.25. The 6-month
continuously compounded zero rate is 1.5%. The 6-month forward price
on the stock is $53.28. Which of the following is true?
1) A risk-free profit can be made by buying the stock and taking a
short forward position.
2) A risk-free profit can be made by taking a short forward position
and a short position in the stock.
3) A risk-free profit can be made by taking a long forward position
and shorting the stock.
4) The forward price is correct and thus no risk-free profit can be
You are using a 2-step binomial tree to price a 2-month American put option with a
strike price of $24 on stock currently worth $22. The tree used to price the option is
shown below. The value indicated at each node is the stock price. The risk-free rate is
5%. The risk-neutral probability of an up move is 51.09%. Calculate the price of the
option at the initial node.
The 1-year futures price for a futures contract on non-dividend-paying stock XYZ is $32.05. The riskfree rate for all maturities is 10%. The price of a 6-month European put option on a 12-month
futures contract with strike price of $30 is $2.45. To be clear, this problem refers to a put option
written on a futures contract. The expiration of the put option is in 6 months. The delivery date of
the futures contract is in 12 months, or 6 months after the time the put option expires. What is the
price of a 6-month European call option written on the same futures contract?
Which of the following is TRUE regarding the implied volatilities of European options written on a
1) For options with the same expiration date, the implied volatility of a call with a strike that is
$5 above the current stock price must be the same as the implied volatility of a put with a
strike price that is $5 below the current stock price.
2) No-arbitrage conditions guarantee that the implied volatility of a call and the implied
volatility of a put with the same strike and expiration must be the same.
3) The implied volatility of all options with the same strike price must be the same, even for
options with different expiration dates. If this is not the case then there is an arbitrage
4) The implied volatility of all options with the same expiration date must be the same, even
for options with different strikes. If this is not the case then there is an arbitrage
A firm will need to purchase machinery from a European manufacturer in August and will have to pay for
the machinery in Euros. To hedge its exposure to the Euro, the firm takes a long position in September
Euro futures contracts at a futures price of $1.13. In August, the firm closes out its futures position at a
futures price of $1.21. The firm then buys Euros in the spot market for $1.20 so that it can pay the
European manufacturer for the machinery. What is the effective exchange rate the firm paid to buy the
Which of the following most accurately describes an asset backed security (ABS)?
1) A short position in a basket of stocks that is intended to hedge against downside risk in
2) A set of assets packaged into a company called a special purpose vehicle (SPV) that sells
different securities, known as tranches, whose cash flows are determined by the cash
flows of the assets owned by the SPV.
3) A portfolio of options that is designed to give exposure only to volatility.
4) An insurance contract that also has positive exposure to the stock market.
Paper#9209210 | Written in 27-Jul-2016Price : $17.85