PROBLEM SET 13
ECO389 – SPRING 2017
Corporate Finance
Instructor: Ramiro Malaga
Due date: Friday 28th, April 2017 at 11:00 p.m.
You will have two attempts, only the last will be valid.
Problem 1
Why does a discounted cash-flow approach to options valuation not work?
A. It is impossible to estimate expected cash flows.
B. One cannot find the appropriate interest rate for an infinitely small
interval.
C. Finding the opportunity cost of capital is impossible as the risk of
options changes every time the stock price moves.
D. The strike price of options changes.
Problem 2
Relative to the underlying stock, a call option always has:
A.
B.
C.
D. A
A
A
A higher beta and a higher standard deviation of return.
lower beta and a higher standard deviation of return.
higher beta and a lower standard deviation of return.
lower beta and a lower standard deviation of return. Problem 3
A call option has an exercise price of $100. At the exercise date, the
stock price could be either $50 or $150. Which investment strategy
provides the same payoff as the stock?
A.
B.
C.
D. Lend PV of
Lend PV of
Borrow $50
Borrow $50 $50
$50
and
and and buy two calls.
and sell two calls.
buy two calls.
sell two calls. Problem 4
Suppose Ralph's stock price is currently $50. In the next six months it
will either fall to $30 or rise to $80. What is the option delta of a
call option with an exercise price of $50?
A.
B.
C.
D. 0.375
0.500
0.600
0.750 Problem 5
A put option on ABC stock currently sells for $4.00. The exercise price
and the stock price is $60. The put option has a delta of 0.5. If within
a short period of time the stock price increases to $60.10, what would
be the change in the price of the put option?
A.
B.
C.
D. Increases
Decreases
Increases
Decreases by
by
by
by $0.05
$0.05
$0.10
$0.10 Problem 6
A call option on ABCD stock, with an exercise price of $50, will either
be worth $12 or worthless. The call option has a delta of 0.3. What is
the binomial spread of possible stock prices? 1 A.
B.
C.
D. Low
Low
Low
Low of
of
of
of $22
$50
$58
$38 and
and
and
and high
high
high
high of
of
of
of $62
$62
$62
$62 Problem 7
What does an equity option's delta reflect?
A.
B.
C.
D. The
The
The
The volatility of the underlying stock price
dividends paid to the underlying stockholders
number of shares needed to replicate one call option
time to expiration Problem 8
Suppose ABCD's stock price is currently $50. In the next six months it
will either fall to $40 or rise to $60. What is the current value of a
six-month call option with an exercise price of $50? The six-month riskfree interest rate is 2% (periodic rate).
A.
B.
C.
D. $5.39
$15.00
$8.25
$8.09 Problem 9
Suppose Carol's stock price is currently $20. In the next six months it
will either fall to $10 or rise to $40.
What is the current value of a six-month call option with an exercise
price of $12? The six-month risk-free interest rate is 5% per six-month
period. [Use the risk-neutral valuation method.]
A.
B.
C.
D. $9.78
$10.28
$16.88
$13.33 Problem 10
Suppose Carol's stock price is currently $20. In the next six months it
will either fall to $10 or rise to $40.
What is the current value of a six-month call option with an exercise
price of $15? The six-month risk-free interest rate is 5% per six-month
period. [Use the replicating portfolio method.]
A.
B.
C.
D. $8.73
$10.28
$16.88
$13.33 Problem 11
The delta of a put option always equals:
A.
B.
C.
D. The
The
The
The delta
delta
delta
delta of
of
of
of an
an
an
an equivalent
equivalent
equivalent
equivalent call
call
call
call option.
option with a negative sign.
option minus one.
option plus one. Problem 12
If the delta of a call option is 0.4, calculate the delta of an equivalent
put option:
A.
B.
C.
D. 0.6.
0.4.
-0.4.
-0.6. 2 Problem 13
Suppose VS's stock price is currently $20. A six-month call option on
VS's stock with an exercise price of $15 has a value of $7.14. What is
the price of an equivalent put option? The six-month risk-free interest
rate is 5% per six-month period.
A.
B.
C.
D. $1.43
$9.43
$8.00
$12.00 Problem 14
If e is the base of natural logarithms, (σ) is the standard deviation
of the continuously compounded annual returns on the asset, and h is the
time to expiration, expressed as a fraction of a year, then the quantity
(1 + upside change) is equal to:
A.
B.
C.
D. e^[(σ) × SQRT(h)].
e^[h × SQRT(σ)].
(σ) × e^[SQRT(h)].
1/(σ) × e^[SQRT(h)]. Problem 15
If the standard deviation of the continuously compounded returns (σ) on
a stock is 40%, and the time interval is a year, then the upside change
equals:
A.
B.
C.
D. 88.2%.
8.7%.
63.2%.
49.2%. Problem 16
The Black-Scholes formula represents the option delta as:
A.
B.
C.
D. d1
N(d1)
d2
N(d2) Problem 17
A European call option with an exercise price of $50 expires in six
months has a stock price of $54 and a continuously compounded standard
deviation of 80%. The risk-free rate is 9.2% per year.
Calculate the value of d2.
A.
B.
C.
D. +0.0657
-0.0657
+0.5657
-0.5657 Problem 18
All else equal, if an option's strike price increases then the:
A.
B.
C.
D. Value
Value
Value
Value of
of
of
of a put option increases and that of a call option decrease.
a put option decreases and that of a call option increase.
both a put option and a call option increase.
both a put option and a call option decrease. Problem 19
The Black-Scholes option pricing model employs which five parameters? 3 A. Stock price, exercise price, risk-free rate, beta, and time to
maturity
B. Stock price, risk-free rate, beta, time to maturity, and variance
C. Stock price, risk-free rate, probability of bankruptcy, variance, and
exercise price
D. Stock price, exercise price, risk-free rate, variance, and time to
maturity
Problem 20
The term [N(d2) × PV(EX)] in the Black-Scholes model represents the:
A.
B.
C.
D. Call option delta.
Bank loan.
Put option delta.
Present value of a bank loan. 4

 

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