Financial Derivatives
Extra Practice 2
Spring 2016
Instructions: All interest rates and rates of inflation are annualized and stated as Annual
Percentage Rates (APRs). Do not round intermediate results as you do the calculations;
but in your answers only, round all dollar figures to the nearest whole cent, and all
interest rates to the nearest basis point (100 basis points equal 1%). Annualize all interest
rates.
Questions 1-5 are multiple-choice with a twist. Circle the letter for the correct
choice, and then write a brief explanation for why the choice is correct in the space
below.
1.
Sophia Rose has 100 shares of Bravo Breakfast Food Company stock that she has
owned for many years. There has been substantial appreciation over that time, so
Sophia would have a large capital gains tax obligation if she were to sell the stock.
Right now the stock is at $50 per share, and Sophia is bullish over the long term;
but she believes the stock will not move very much in the next few months (just
bounce randomly up and down around the current price). Sophia would like to
generate some cash flow from owning the stock. Which of the following would be
a potentially profitable strategy (if Sophia is right about the short-term prospects for
the stock)?
a. Buy both calls and puts with exercise price of $50 and June expiration.
b. Sell a 100-share contract for June 50 puts and buy a 100-share contract for July
50 calls.
c. Buy 100-share contracts for the July 45 calls (exercise price $45) and the July
55 calls (exercise price $55). Sell two 100-share contracts for the July 50 calls
(exercise price $50).
2.
Option A is a put option written on Digital Dynamics Company, with exercise price
of $45. Option B is also a put option on Digital, with exercise price of $50. Both
options expire six months from now. Which of the following is a theoretically correct
relationship?
a. Option A is worth more than Option B.
b. Option B is worth more than Option A.
c. Option B is worth the same as Option A.
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3.
Malcolm Eisennagel works in the headquarters of Delta Chemicals Company. The
stock is presently at $70 per share. A moment ago he overheard parts of a hushed
conversation between the Chief Executive and the Chief Financial Officer. He now
knows that there will be a press release this afternoon that the executives seem to
think will cause a substantial movement in the stock price, but he didn’t hear
enough to know whether the stock will go up or down. Malcolm has a trading
account that allows him to book option trades online. Which of the following would
be a potentially profitable strategy (if Malcolm’s understanding is correct about the
short-term prospects for the stock)?
a. Buy 100-share contracts for the July 75 calls and the July 65 calls (these have
exercise prices of $75 and $65, respectively). Sell two 100-share contracts for
the July 70 calls (exercise price $70, with July expiration).
b. Sell a 100-share contract for July 70 puts and buy a 100-share contract for July
70 calls.
c. Buy both calls and puts with exercise price of 70 and July expiration.
4.
Option A is a call option written on Alpha Chemicals Company stock, with
expiration in six months. Option B is a call on Alpha with expiration in five
months. Both options have an exercise price of $45 per share. Which of the
following is a theoretically correct relationship?
a. Option A is worth more than Option B.
b. Option B is worth more than Option A.
c. Option B is worth the same as Option A.
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5.
Alpha Chemicals Company stock fell by 15¢, from $35.50 to $35.35. Calvin
Smiley owns call options on Alpha, which he bought three months ago. They
expire in October 2016, and have an exercise price of $25. Which of the following
is a theoretically possible response for the option value (on a per-share basis), to the
recent move of the stock?
a. fall by 16¢
b. rise by 3¢
c. fall by 12¢.
d. rise by 20¢.
e. None of the above is possible.
For questions 6-11, write your answers in the left-hand margin. There is no need to
show work.
6.
Digital Datawhack stock just rose by 10¢, from $65 to $65.10 per share. If the
August 60 Datawhack calls ($60 exercise price) have Delta of 0.70, what change
would you expect to see in the price of the option?
7.
Suppose the stock price is $50 and the present value of the exercise price is $43.75.
Delta is 0.70. Also, the change in value of the call relative to a small change in the
present value of the exercise price is 0.60. The stock pays no dividends. Volatility
of the stock is 60%. Based on this information, estimate the premium for the call
option.
8.
Refer to question 7. Find the value of a put with the same exercise price and the
same values as the call in all other respects.
9.
Suppose wheat is $5.8875 per bushel in the spot market. Storage cost in a bonded,
insured warehouse is $0.45 per bushel (prepaid) for a 180-day period. Interest is
1.35% compounded continuously on U.S. Treasury bills with 180 days to maturity.
Find the equilibrium “cost of carry” futures price for wheat to be delivered 180 days
from now (assuming wheat pays no dividend in any way).
10.
Suppose the exercise price of an option is $85, the Treasury Bill rate is 1.25%, and
there are 220 days remaining until expiration (365-day year). Discounted
continuously, what is the present value of the exercise price?
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11.
The following prices are observed:
•
Euro per Dollar exchange rate is 0.93 spot and 0.90 for 180-day forward
($1 = € 0.93 spot and $1 = € 0.90 forward).
•
German interest rate is 2.00% compounded daily (365-day year).
•
U.S. stock market index is 2108 today.
•
At today's level of the index, the average annual dividend yield on the stocks
in the index is 2% (for simplicity assume you’ll receive half the annual
dividends during your six-month holding period, and these dividends will all
be paid at the end of 180 days).
•
Find the equilibrium futures price for the stock index 180-day contract. (Use
daily compounding.)
For questions 12-16, show work in the space provided below the question.
12.
The following prices are observed:
• Myron Labs stock is selling for $48 per share.
• Call options on Myron Labs with exercise price 40, and June expiration, are
selling for $10.40 per share.
• Put options on Myron Labs with exercise price 40, and June expiration, are
selling for $2.40 per share.
• At the current T-Bill rate, $39.80 would grow to $40 at the expiration date of
the options.
SHOW WORK: Formulate an arbitrage strategy to profit from the situation (ignoring
transactions costs). Give a brief explanation in the space below. Explain your strategy in
terms of a volume of one share.
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13.
Acme stock is $75 per share. The premium for the Acme July 70 call option is
$8.90 per share (the July 70 calls expire in July with an exercise price of $70). The
premium for the July 75 call is $6.00 per share. The premium for the July 80 call is
$4.15 per share.
Arnold Bradbury is an options trader. You have just observed him buying 2000
of the July 75 calls while simultaneously selling 1000 of the July 70 calls and
selling 1000 of the July 80 calls.
What has to happen at the end of the holding period in order for this position to
be profitable? (Assume Arnold would hold the position until expiration.)
SHOW WORK: explain in the space below.
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14.
The following prices are observed. Formulate an arbitrage strategy to profit from
the situation (ignoring transactions costs).
• VierPunkt stock is selling for $100 per share.
• Call options on VierPunkt at 90, with expiration in nine months, are selling for
$30 per share.
• Call options on VierPunkt at 100, with expiration in nine months, are selling
for $28.00 per share.
• Put options on VierPunkt at 90, with expiration in nine months, are selling for
$21.00 per share.
• Put options on VierPunkt at 100, with expiration in nine months, are selling for
$25.00 per share.
• At the current T-Bill rate, $88.68 invested today would grow to $90 (and
$98.54 would grow to $100) at the expiration date of the options.
SHOW WORK: explain in the space below.
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15.
Suppose the expiration is in one year, the exercise price is $80 and the T-bill rate is
1.005%. The underlying stock, Holloworth Mines, is currently selling for $79.20
per share. Standard deviation of returns (sigma, also called volatility) for the
underlying stock is 60% (0.60). The stock pays no dividends. Based on this
information, estimate the per-share premium for the call option with Holloworth
Mines as the underlying asset, expiration in one year, and exercise price of $80.
Use the Black-Scholes Option Pricing Model. In order to find the area under the
Normal Probability curve, use the attached tables.
SHOW WORK: explain in the space below.
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16.
All of the information in problem 15 applies here as well. Find the per-share
market value for a put option (put premium).
SHOW WORK: explain in the space below.