Transcript
Chapter Six
The Black-Scholes Option Pricing Model
Multiple Choice
In the Black-Scholes Option Pricing Model, what is the minimum and maximum value of N(d1)?
minus infinity to plus infinity
minus infinity to zero
minus one to zero
zero to plus infinity
ANSWER: A
In the Black-Scholes Option Pricing Model, if interest rates rise, the price of a call option will
decline.
remain unchanged.
increase.
decline, then increase.
ANSWER: C
All of the following are assumptions of the Black-Scholes Option Pricing Model except
markets are efficient.
no dividends.
interest rates are constant.
investors are generally bullish.
ANSWER: D
The expected volatility of the underlying asset is known as
sigma.
delta.
gamma.
theta.
ANSWER: A
Option value is mostly concerned with
historical volatility
average daily volatility.
expected future volatility.
market average volatility.
ANSWER: C
If volatility increases, call premiums _____ and put premiums _____.
increase, increase
increase, decrease
decrease, increase
decrease, decrease
ANSWER: A
A method of adjusting for cash dividends is the _____ model.
Fisher
Sharpe
Merton
Miller
ANSWER: C
Everything else being equal, an American option will sell for ________ a European option.
more than
less than
the same as
None of the above; cannot be determined
ANSWER: A
The Black-Scholes model assumes a _____ distribution.
lognormal
uniform
triangular
Poisson
ANSWER: A
Which of the following is most accurate?
Implied volatility is usually less than historical volatility.
Implied volatility is usually greater than historical volatility.
Implied volatility is usually equal to historical volatility.
There is no reliable connection between historical and implied volatility.
ANSWER: D
Option traders often price options in _____ units.
delta
volatility
theta
Eurodollar
ANSWER: B
The plot of implied volatility values as a function of the stock price is known as a
yield curve.
volatility smile.
volatility decay plot.
volatility diffusion diagram.
ANSWER: B
The option to defer something is an example of a(n) _____ option.
exotic
lookback
real
barrier
ANSWER: C
The Black-Scholes model works best with options that are
deep out-of-the-money.
out-of-the-money
at-the-money
in-the-money.
ANSWER: C
Short Answer/Problem
A non-dividend paying stock sells for $23 3/8. What is the theoretical value of a European style, $25 call with 50 days until expiration, assuming interest rates of 6% and annual volatility of 25%?
ANSWER: Using the CBOE options calculator, the theoretical value is $0.35.
Estimate the value of the option in Problem 1 if it were American style instead of European.
ANSWER: An American option should sell for more than a European option. The CBOE calculator indicates a theoretical value of $0.36.
You are going to use the Black-Scholes option pricing model on a six-month call option that has the following expected dividend stream; short term interest rates are 5%.
Time until dividend
2 months
5 months
8 months
Expected dividend
$1.00
$1.00
$1.05
If the current stock price is $105, what is the adjusted stock price you would use as a BSOPM input?
ANSWER:
Only dividends over the option’s life matter. S’ = S – PV (dividends)
$103.13
