Fundamentals of Derivatives Markets (McDonald)
Chapter 11 The Black–Scholes Formula
11.1 Multiple Choice Questions
1) What is the price of a $35 strike call? Assume S = $38.50, σ = 0.25, r = 0.06, the stock pays no
dividend and the option expires in 45 days?
A) $3.50
B) $3.65
C) $3.80
D) $3.95
2) What is the price of a $60 strike put? Assume S = $63.75, σ = 0.20, r = 0.055, the stock pays no
dividend and the option expires in 50 days?
A) $0.66
B) $0.55
C) $0.44
D) $0.33
3) What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a
2.5% continuous dividend and the option expires in 45 days?
A) $0.60
B) $0.50
C) $0.40
D) $0.30
4) What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock pays a
1.0% continuous dividend and the option expires in 110 days?
A) $2.70
B) $2.10
C) $1.80
D) $1.20
5) What is the delta on a $20 strike call? Assume S = $22.00, σ = 0.30, r = 0.05, the stock pays a
1.0% continuous dividend and the option expires in 80 days?
A) 0.790
B) 0.820
C) 0.850
D) 0.880
6) What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock pays a
2.0% continuous dividend and the option expires in 40 days?
A) 0.582
B) 0.602
C) 0.662
D) 0.702
7) Assume that a $50 strike call has a 3.0% continuous dividend, σ = 0.27, r = 0.06 and 60 days
from expiration. What is the gamma for a stock price movement from $48.00 to $49.00?
A) 0.046
B) 0.074
C) 0.089
D) 0.099
8) 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
9) Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar
denominated pound call is $1.30. Assume r = 0.045, rf = 0.06, σ = 0.15 and the option expires
in 180 days. What is the call option price?
A) $0.133
B) $0.143
C) $0.153
D) $0.163
10) Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar
denominated pound put is $1.20. Assume r = 0.04, rf = 0.05, σ = 0.20 and the option expires in
270 days. What is the put option price?
A) $0.075
B) $0.085
C) $0.095
D) $0.105
11) Suppose the 180–day futures price on gold is $110.00 per ounce and the volatility is 20.0%.
Assume interest rates are 3.5%. What is the price of a $120 strike call futures option that
expires in 180 days?
A) $1.89
B) $2.19
C) $2.59
D) $3.09
12) Suppose the 120–day futures price on gold is $115.00 per ounce 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
13) Assume that a $60 strike call has a 2.0% continuous dividend, r = 0.05, and the stock price is
$61.00. What is the theta of the option as the expiration time declines from 60 to 50 days?
A) –0.52
B) –0.42
C) –0.32
D) –0.22
14) Assume that a $75 strike call has a 1.0% continuous dividend, 90 days until expiration and
stock price of $72.00. What is the rho of the option as the interest rate changes from 6.0% to
5.0%?
A) 0.07
B) 0.12
C) 0.16
D) 0.20
15) Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend.
Assume S = $58.50, σ = 0.25, and r = 0.06. What is the option elasticity given an immediate
price increase of $1.50?
A) 24.61
B) 18.61
C) 14.61
D) 9.61
16) Assume that an investor is currently holding a reverse straddle position (i.e. a short put and
short call), which is currently a profitable investment. All else being equal, what would this
investor like to happen to vega?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
17) If an investor is speculating with a long call position, what is the most likely preference of
the investor, relative to a change in rho?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
18) As the date of expiration approaches, what change in theta might counteract or slowdown
the drop in the option price?
A) Decrease
B) Increase
C) Stay constant
D) Indifferent
19) What is the total dollar cost to create a delta hedge position against a 200 short call position?
Assume calls are priced at $4.16, the delta is 0.7644, and stock price is $73.00.
A) $9,880
B) $10,328
C) $11,168
D) $12,660
20) Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68 days until
expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises
to $34.50?
A) $9.23 loss
B) $9.23 gain
C) $7.62 loss
D) $7.62 gain
21) Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and the
stock price is $48.00. What is the profit or loss, per share, for a short put position if the option
expires in 60 days and the price rises to $50.00 after 5 days?
A) $1.05 loss
B) $1.05 gain
C) $1.12 gain
D) $1.12 loss
22) Assume S = $33.00, σ = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike puts at 68 days until
expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises
to $34.50? Assume no cost to short stock.
A) $8.30 gain
B) $8.30 loss
C) $9.56 gain
D) $9.56 loss
23) 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
24) Which Greek is also called the time decay?
A) Delta
B) Rho
C) Theta
D) Vega
25) What Greek will a trader be most interest in if she is buying and selling volatility index
options?
A) Delta
B) Rho
C) Theta
D) Vega
26) The Greek that is also called the Hedge Ratio is the ________.
A) Delta
B) Rho
C) Theta
D) Vega
27) A trader who monitors which Greek is most likely to pay close attention to the actions of the
Federal Reserve Board?
A) Delta
B) Rho
C) Theta
D) Vega
28) What is the only unobservable variable in the Black Scholes model?
A) Exercise price
B) Interest rates
C) Stock price
D) Volatility
29) Given the following data, what is the approximate implied volatility? Assume S = $38.50, K =
$40, r = .06, Call price = $1.60 the stock pays no dividend and the option expires in 45 days.
A) 21 %
B) 32 %
C) 39 %
D) 44 %
30) Given the following data, what is the approximate implied volatility? Assume S = $41, K =
$40, r = .08, Call price = $2.70 the stock pays no dividend and the option expires in 90 days.
A) 21 %
B) 32 %
C) 39 %
D) 44 %
11.2 Short Answer Essay Questions
1) Which Greek is also called time decay and why?
6
2) Draw a payoff diagram for a long put position, depicting options that expire at 0, 30 and 60
days.
Answer:
3) What is the difference between a standard bull spread and a calendar bull spread?
4) What is the difference between implied volatility and historical volatility?
5) What prevents a market–maker from readjusting her delta hedge on a continual basis?
11.3 Class Discussion Question
1) Why do we care about Greeks? Use this as an opportunity to introduce students to option
strategies. Ask students to create simple strategies such as covered calls. Introduce Greeks
and show how “not all covered calls are created equal.” Encourage the class to explain how
the Greeks tell us which options are better to use than others.