Chapter 18 Option Valuation and Strategies
TRUE/FALSE
model, the value of a call option rises as it approaches
expiration.
model, the value of a call option rises as interest rates
increase.
option’s strike price by the probability that the option
will be exercised.
of a stock, a call and a put on that stock, and a debt
instrument maturing at the expiration of the options must
equal zero.
rates by the Federal Reserve affects stock and option
prices.
overpriced, the investor should sell the stock short, sell
the put, buy the call, and buy the bond.
that is necessary to offset price movements in the
underlying stock.
necessary to offset a long position in a stock is 7.0.
the Black/Scholes option valuation model.
is protected from a large increase in the price of the
stock by selling a call option.
price and expiration date is an illustration of a straddle.
stock prices.
short position.
an increase in the price of a stock.
options with the same expiration dates.
fluctuate but they are not certain as to the direction,
these investors may buy a straddle.
in one option and a short position in another option with a
different strike price.
option and shorts the stock.
results as buying a stock and a put.
produces the same returns as buying a stock.
MULTIPLE CHOICE
model, the value of a call option increases if
a. the option approaches expiration
b. the return on the stock is more certain
c. interest rates on a discounted bond decline
d. the standard deviation of the stock’s
return increases
model, a call option’s value increases if
a. stock prices increase and interest rates decrease
b. the time to expiration decreases and interest
rates increase
c. the variability of the stock’s return increases
and stock prices increase
d. interest rates decrease and the variability of
the stock’s return increases
model, a call option’s value decreases if
a. interest rates increase as the option approaches
expiration
b. the variability of the stock’s return declines
and the interest rate decreases
c. an increase in the price of the stock results in
a two for one stock split
d the option is exercised
a. the sum of the prices of a stock and a call
equal zero
b. the sum of the prices of a put and a call
equal zero
c. the sum of the prices of a stock, a call, a put,
and a bond equal zero
c. sum of the prices of a stock and a put must equal
the sum of the prices of a call and a discounted
bond with the maturity date as the expiration
date of the options
that the investor should
a. sell the call and the stock and buy the put and
the bond
b. sell the call and the bond and buy the put and
the stock
c. sell the bond and the put and buy the stock and
the call
d. sell the stock and the put and buy the call and
the bond
a. the number of call options to offset movements in
the price of the stock
b. the number of call options to offset a straddle
c. the number of put options to offset movements in
the price of a call option
d. the number of call options to offset the impact
of changes in interest rates
reduces the risk of loss by
a. buying a put
b. buying a call
c. entering a limit order to sell the stock if its
price declines
d. increasing the collateral with the broker
a. buys stock and a call
b. buys two calls with different strike prices
c. buys a put and sells a call with the same
strike price
e. buys a put and buys a call with the same
strike price
will be stable, he or she may
a. sell a straddle
b. buy a straddle
c. buy a call
d. buy a put
stock will fluctuate, this individual may
a. sell a call and sell a put
b. buy a call and buy a put
c. buy a call and sell a put
d. sell a call and buy a put
anticipates
a. higher interest rates
b. higher option prices
c. lower stock prices
d. lower put prices
anticipates
a. higher call price
b. higher stock prices
c. lower stock prices
d. lower call prices
a. an index of option prices
b. an index of Black/Scholes option values
c. positively correlated with the S&P 500
d. a measure of investor sentiment
a. increased stock returns
b. increased stock market volatility
c. increased interest rates
d. increased market complacency
PROBLEMS
1. A call option is the right to buy stock at $25 a share.
According to the Black/Scholes option valuation model, what
is the value of the call
a. if the price of the stock is $25, the interest rate
is 8 percent, the option expires in three months, and the
standard deviation of the stock’s return is 0.20 (20
percent)?
b. if the price of the stock is $25, the interest rate
is 6 percent, the option expires in three months, and the
standard deviation of the stock’s return is 0.20 (20
percent)?
c. if the price of the stock is $27, the interest rate
is 8 percent, the option expires in three months, and the
standard deviation of the stock’s return is 0.20 (20
percent)?
2. If the price of a stock is $100 while the price of a
call option at $100 is $3, the price of the put option is
$2, and the rate of interest is 10 percent so the investor
can purchase a $100 discounted note for $90.90 (i.e., $91).
what should you do and verify the potential losses and
profits from the position.
3. The investor owns 1,000 shares of stock but anticipates
its price may decline. To reduce the risk of loss, how many
call options must be sold if the hedge ratio is 0.7?
4. A put and a call have the following terms:
Call: strike price $30
term three months
price $3
Put: strike price $30
term three months
price $4
The price of the stock is currently $29. You sell the stock
short and purchase the call. Complete the following table and
answer the questions.
Price of Profit on Profit on Net profit
the stock stock put
$20
25
30
35
40
a. What is the maximum possible profit on the position?
b. What is the maximum possible loss on the position?
c. What is the range of stock prices that generates a profit?
d. What advantage does this position offer?
5. The price of a stock is $46 and the prices of call
options to buy the stock at $45 and $50 are $6 and $3,
respectively. What are the potential profits and losses
when the price of the stock is $40, $45, $50, and $55 if
the investor buys the call at $45 and sells the call at
$50?
6. If a stock is selling for $33 and you expect the price
not to fluctuate, what are the potential profits and losses
from writing a straddle if a call option at $35 sells for
$3 and the put option at $35 sells for $4?
7. Put-call parity basically says that combination of a put,
a call, and a risk-free bond must be the same value as the
underlying stock. If not, at least one market is in
disequilibrium. The resulting arbitrage alters the
securities’ prices until the value of the call plus the bond
is equal to the prices of the put plus the stock. Currently,
the price of a stock is $100 while the price of a call option
at $100 is $10; the price of the put option is $4.59, and the
rate of interest is 8 percent, so that the investor may
purchase a $100 discounted note for $92.59.
a. Do these prices indicate that the financial markets are in
equilibrium? Show me how you derived your answer.
b. An arbitrage opportunity should exist, but if you set up
the position incorrectly, you will always sustain losses.
Verify to me that if you do set up an incorrect arbitrage,
you will always sustain a loss. Please use prices of the
stock at $80, $100, and $120 as of the expiration date of the
options.
8. Put-call parity asserts that a combination of a long
position in the stock and the put produces the same return as
a comparable position in a call and a risk-free bond. If not,
at least one market is in disequilibrium. The resulting
arbitrage alters the securities’ prices until the value of
the stock plus the put equals the prices of the call and the
bond. The successful use of arbitrage assumes the investor of
a profit no matter what happens to the price of the stock.
Put-call parity also asserts that if an arbitrage opportunity
does not exist, then a combination of the stock and the put
produces the same return as the comparable position in the
call and the risk-free bond. Currently, the price of a stock
is $70 while the price of a call option at $70 is $6; the
price of the put option at $70 is $2, and the price of a
discounted bond is $66. Verify that a long position in the
stock and the put produces the same performance as a long
position in the call and the bond for the following prices of
the stock: $60, 65, 70, 75, and 80.
SOLUTIONS TO PROBLEMS
