Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
Which of the following statements is false?
1)
A)
The Black–Scholes formula can be used to price American or European call options on
non–dividend–paying stocks.
B)
We can use the Black–Scholes formula to compute the price of a European put option on a
non–dividend–paying stock by using the put–call parity formula.
C)
If you take the option price quoted in the market as an input and solve for the volatility you
will have an estimate of a stock’s volatility known as the implied volatility.
D)
We need to know the expected return on the stock to calculate the option price in the
Black–Scholes Option Pricing Model.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
2)
Assuming the Beta on KD stock is 1.1, the calculated beta for a one–year call option on KD stock
with a strike price of $20 is closest to:
2)
A)
–7.7
B)
4.6
C)
2.4
D)
–1.8
3)
Using the binomial pricing model, the calculated price of a one–year put option on KD stock with a
strike price of $20 is closest to:
3)
A)
–7.7
B)
4.6
C)
–1.8
D)
2.4
4)
Using risk neutral probabilities, the calculated price of a one–year put option on KD stock with a
strike price of $20 is closest to:
4)
A)
$2.15
B)
$2.40
C)
$1.45
D)
$2.00
5)
Consider the following equation:
B =Cd– Sd
1 + rf
In this equation, the term B, represents
5)
A)
the bid price for the option.
B)
the number of shares of stock to buy for the replicating portfolio.
C)
the highest price at which it is advantageous to buy the option.
D)
the position in bonds for the replicating portfolio.
6)
Which of the following statements is false?
6)
A)
Because a stock’s volatility is much easier to measure (and forecast) than its expected return,
the Black–Scholes formula can be very precise.
B)
Because a leveraged position in a stock is riskier than the stock itself, this implies that call
options on a positive beta stock are more risky than the underlying stock and therefore have
higher returns and higher betas.
C)
Only one parameter input for the Black–Scholes formula, the volatility of the stock price, is
not observable directly.
D)
The option delta, , has a natural interpretation: It is the change in the price of the stock given
a $1 change in the price of the option.
7)
Consider the following equation:
C = S × N
ln S
PV(K)
T+T
2–PV(K) ×N
ln S
PV(K)
T+T
2– T
In this equation, the term represents
7)
A)
the annual volatility of the stock.
B)
the number of days to expiration.
C)
the expected return on the stock.
D)
the number of years to expiration.
8)
Which of the following statements is false?
8)
A)
When using the Binomial Option Pricing Model, by the Law of One Price, the price of the
option today must equal the current market value of the replicating portfolio.
B)
We define the state in which the stock price goes up as the up state and the state in which the
stock price goes down as the down state.
C)
We can summarize the payoffs for the Binomial Option Pricing Model in a binomial tree–a
timeline with two branches at every date that represent the possible events that could happen
at those times.
D)
The techniques of the binomial option pricing model are specific to European call and put
options.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
9)
Using the binomial pricing model, the calculated price of a one–year call option on KD stock with a
strike price of $20 is closest to:
9)
A)
$2.15
B)
$1.45
C)
$2.40
D)
$2.00
10)
Which of the following statements is false?
10)
A)
The binomial tree contains all the information we currently know: the value of the stock,
bond, and call options in each state in one period, as well as the price of the stock and bond
today.
B)
By using the Law of One Price, we are able to solve for the price of the option as long as we
know the probabilities of the states in the binomial tree.
C)
The idea that you can replicate the option payoff by dynamically trading in a portfolio of the
underlying stock and a risk–free bond was one of the most important contributions of the
original Black–Scholes paper. Today, this kind of replication strategy is called a dynamic
trading strategy.
D)
A replicating portfolio is a portfolio of other securities that has exactly the same value in one
period as the option.
11)
Consider the following equation:
E=A
E
U=1+D
E
U
the term refers to
11)
A)
the marginal tax rate.
B)
the number of shares of stock to buy for the replicating portfolio.
C)
the change in the debt–to–value ratio.
D)
the change in the debt–to–equity ratio.
12)
Which of the following statements is false?
12)
A)
If all market participants were risk neutral, then all financial assets (including options) would
have the same cost of capital–the risk free rate of interest.
B)
In both the Binomial and Black–Scholes Pricing Models, we need to know the risk neutral
probability of each possible future stock price to calculate the option price.
C)
Because no assumption on the risk preferences of investors is necessary to calculate the option
price using either the Binomial Model or the Black–Scholes formula, the models must work
for any set of preferences, including risk–neutral investors.
D)
In the real world, investors are risk averse. Thus, the expected return of a typical stock
includes a positive risk premium to compensate investors for risk.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
13)
Using the binomial pricing model, the calculated price of a one–year put option on KD stock with a
strike price of $20 is closest to:
13)
A)
$1.45
B)
$2.40
C)
$2..15
D)
$2.00
14)
Which of the following statements is false?
14)
A)
If we let A be the value of the firm’s assets, E be the value of equity, and D be the value of
debt, then because equity is a call option on the assets of the firm, E = S +B with A = E + D =
S.
B)
Equity can be viewed as a call option on the firm’s assets.
C)
For companies with high debt–to–equity ratios, the approximation that the beta of debt is
zero is unrealistic; such corporations have a positive probability of bankruptcy, and this
uncertainty usually has systematic components.
D)
When the debt is risky, the firm’s equity is always in–the–money; thus = 1.
15)
Consider the following equation:
D= (1 – A
D
U= (1 – 1 +E
D
U
the term
D refers to
15)
A)
the beta for the firm’s equity.
B)
the beta for the firm’s debt.
C)
the unlevered beta for the firm’s debt.
D)
the beta of the firm’s assets.
16)
Which of the following statements is false?
16)
A)
Out–of–the–money calls have the highest expected returns and out–of–the–money puts have
the lowest expected returns.
B)
The beta of a portfolio is just the weighted average beta of the constituent securities that make
up the portfolio.
C)
The magnitude of the leverage ratio for options is usually very small, especially for
out–of–the–money options.
D)
The expression S/(S +B) is the ratio of the amount of money in the stock position in the
replicating portfolio to the value of the replicating portfolio (or the option price); it is known
as the leverage ratio.
out–of–the–money options.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
17)
The risk neutral probability of a down state for KD industries is closest to:
17)
A)
40.0%
B)
60.0%
C)
37.5%
D)
62.5%
18)
Consider the following equation:
C = S × N
ln S
PV(K)
T+T
2–PV(K) ×N
ln S
PV(K)
T+T
2– T
In this equation, the term S represents
18)
A)
strike price for the option.
B)
the stock price at expiration.
C)
the current price of the stock.
D)
the annual volatility of the stock.
19)
You would like to know the beta of debt for KT Industries. The value of KT’s outstanding equity is
$50 million, and you have estimated its beta to be 1.62. You cannot, however, find enough market
data to estimate the beta of tis debt, so you decide to use the Black–Scholes formula to find an
approximate value for the debt. KT has a five year zero coupon bond outstanding with a market
value of $80 million. If you estimated from the Black–Scholes model is .60, then the beta for KT’s
debt is closest to:
19)
A)
2.70
B)
0.90
C)
0.59
D)
1.00
20)
Consider the following equation:
option =S
S+ B
S+B
S+ B
B
The term B
S+ B
B is
20)
A)
could be positive or negative depending on whether the option in question is a put or a call.
B)
always positive since B is always positive.
C)
always negative since B is always negative.
D)
always equal to zero since
B= 0.
21)
Which of the following statements is false?
21)
A)
To ensure that all assets in the risk–neutral world have an expected return equal to the
risk–free rate, relative to the true probabilities, the risk–neutral probabilities underweight the
bad states and overweight the good states.
B)
After we have constructed the tree and calculated the probabilities in the risk–neutral world,
we can use them to price the derivative by simply discounting its expected payoff (using the
risk neutral probabilities) at the risk–free rate.
C)
By using the probabilities in the risk–neutral world we can price any derivative security–that
is, any security whose payoff depends solely on the prices of other marketed assets.
D)
In Monte Carlo simulation, the expected payoff of the derivative security is estimated by
calculating its average payoff after simulating many random paths for the underlying stock
price.
22)
Which of the following is not an input required by the Black–Scholes option pricing model?
22)
A)
The risk–free interest rate
B)
The expected volatility of the stock
C)
The expected return on the stock
D)
The current stock price
23)
Consider the following equation:
E=A
E
U=1+D
E
U
the term
U refers to
23)
A)
the unlevered beta for the firm’s debt.
B)
the beta of the firm’s assets.
C)
the beta for the firm’s debt.
D)
the beta for the firm’s equity.
24)
Which of the following statements is false?
24)
A)
The beta of a put option written on a negative beta stock is always negative.
B)
For a call written on a stock with positive beta, the beta of the call always exceeds the beta of
the stock.
C)
As the stock price changes, the beta of an option will change, with its magnitude falling as the
option goes in–the–money.
D)
A put option is a hedge, so its price goes up when the stock price goes down.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
25)
Using risk neutral probabilities, the calculated price of a one–year call option on KD stock with a
strike price of $20 is closest to:
25)
A)
$2.40
B)
$2.15
C)
$1.45
D)
$2.00
26)
The risk neutral probability of an up state for KD industries is closest to:
26)
A)
62.5%
B)
37.5%
C)
40.0%
D)
60.0%
27)
Which of the following statements is false?
27)
A)
The Black–Scholes formula is derived assuming that the call is a European option.
B)
Of the five required inputs in the Black–Scholes formula, four are directly observable.
C)
The Black–Scholes Option Pricing Model can be derived from the Binomial Option Pricing
Model by making the length of each period, and the movement of the stock price per period,
shrink to zero and letting the number of periods grow infinitely large.
D)
N(d) is the cumulative normal distribution–that is, the probability that a normally distributed
variable is greater than d.
28)
Consider the following equation:
C = S × N
ln S
PV(K)
T+T
2–PV(K) ×N
ln S
PV(K)
T+T
2– T
In this equation, the term T represents
28)
A)
the number of years to expiration.
B)
the number of days to expiration.
C)
the expected return on the stock.
D)
the annual volatility of the stock.
29)
Consider the following equation:
=Cu– Cd
Su– Sd
In this equation, the term , represents
29)
A)
the position in bonds for the replicating portfolio.
B)
the change in the stock price from the high state to the low state.
C)
the change in the stock price from the low state to the high state.
D)
the number of shares of stock to buy for the replicating portfolio.
N(d) is the cumulative normal distribution–that is, the probability that a normally
30)
Risk neutral probabilities are also known as all of the following except
30)
A)
martingale prices.
B)
state–contingent prices.
C)
contingent probabilities.
D)
state prices.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
Use the information for the question(s) below.
The current price of Kinston Corporation stock is $10. In each of the next two years, this stock price can wither go up by $3.00
or go down by $2.00. Kinston stock pays no dividends. The one year risk–free interest rate is 5% and will remain constant.
31)
Using the binomial pricing model, calculate the price of a two–year put option on Kinston stock with a strike
price of $9.
32)
Using risk neutral probabilities, calculate the price of a two–year call option on Kinston stock with a strike price
of $9.
Use the information for the question(s) below.
The current price of KD Industries stock is $20. In the next year the stock price will either go up by 20% or go down by 20%.
KD pays no dividends. The one year risk–free rate is 5% and will remain constant.
33)
Construct a binomial tree detailing the option information and payoffs for a call option with a $20 strike price
that expires in one year.
Use the information for the question(s) below.
The current price of Kinston Corporation stock is $10. In each of the next two years, this stock price can wither go up by $3.00
or go down by $2.00. Kinston stock pays no dividends. The one year risk–free interest rate is 5% and will remain constant.
34)
Using the binomial pricing model, calculate the price of a two–year call option on Kinston stock with a strike
price of $9.
35)
Luther Industries does not pay dividend and is currently trading at $25 per share. The current risk–free rate of
interest is 5%. Calculate the price of a call option on Luther Industries with a strike price of $30 that expires in
75 days when N(d1) = .639 and N(d2) = .454.
Use the information for the question(s) below.
The current price of Kinston Corporation stock is $10. In each of the next two years, this stock price can wither go up by $3.00
or go down by $2.00. Kinston stock pays no dividends. The one year risk–free interest rate is 5% and will remain constant.
36)
Using risk neutral probabilities, calculate the price of a two–year put option on Kinston stock with a strike price
of $9.
Answer Key
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Answer Key
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