Transcript
Chapter Five
Option Pricing
Multiple Choice
If a stock’s variance of return increases and everything else remains constant, the price of a call option will
decline.
remain unchanged.
increase.
gradually increase.
ANSWER: C
XYZ pays no dividends and sells for $50. There is a one-year call to buy 100 shares at $50 selling for $4.00. If interest rates are 6%, what should a one-year put sell for?
$1.17
$1.25
$1.34
$1.56
ANSWER: A
XYZ pays no dividends and sells for $50. There is a one-year call to buy 100 shares at $50 selling for $3.75. If interest rates are 6%, what should a one-year put sell for?
$0.92
$1.17
$1.34
$1.56
ANSWER: A
A person holds 2 XYZ APR 60 calls. What is their holding after a 2 for 1 stock split?
2 XYZ APR 60 calls
4 XYZ APR 30 calls
2 XYZ APR 30 calls
4 XYZ APR 60 calls
ANSWER: B
For at-the-money stock options, put/call parity requires that, for otherwise similar options,
puts sell for more than calls.
puts sell for the same price as calls.
puts sell for less than calls.
puts sell for at least as much as calls.
ANSWER: C
The Black-Scholes option pricing model was developed in _____.
1887
1923
1973
1987
ANSWER: C
Finance is sometimes called the study of
arbitrage.
parity relationships.
equal value.
riskless relationships.
ANSWER: A
According to pricing theory, a long stock position is most similar to
a short call and a short put.
a short call and a long put.
a long call and a short put.
a long call and a long put.
ANSWER: C
A covered call is most similar to
a long call.
a long put.
a short call.
a short put.
ANSWER: D
The value of a call option depends on all of the following except
the expected return on the underlying asset.
the current interest rate.
the life of the option.
the volatility of the underlying asset.
ANSWER: A
If interest rates rise, the price of a call ___ and the price of a put ___.
increases, increases
increases, decreases
decreases, increases
decreases, decreases
ANSWER: B
Short essay/problems
Comment on the following statement: “It seems to me that with at-the-money options on a given stock, the calls usually sell for more than the puts.”
ANSWER: This is true because of put/call parity.
Suppose you look in the newspaper and see that an option has changed price since yesterday, but the stock price has remained the same. Explain three factors that could cause the option premium to change while the stock price remains unchanged.
ANSWER: Interest rates could have changed, time passed, and anticipated future volatility might have changed. It is also possible that dividend expectations could have changed.
Briefly explain, in words, why the price of a put option and the price of a call option on the same stock are not independent.
ANSWER: The put/call parity model shows that arbitrage opportunities can be present if the two types of options have their values determined independently of each other.
XYZ Corporation sells for $35 per share; the AUG option series has exactly six months until expiration. At the moment, the AUG 35 call sells for $3, and the AUG 35 put sells for $1 3/8. Using this information, what annual interest rate is implied in the prices?
ANSWER:
C – P = S – K/(1+R)T
3 – 1.375 = 35 – 35/(1 + R).5
1.625 – 35 = -35/(1 + R).5
33.375 = 35/(1 + R).5
1.0487 = (1 + R).5
R = 9.97%
List four reasons why the price of a put option might go down.
ANSWER: The stock price rises; time passes; volatility expectations decrease; interest rates rise.
Indicate whether the option premium will rise or fall:
Increase in interest rates
Call
_____
Put
_____
Decrease in time until expiration
Call
_____
Put
_____
Decrease in stock volatility
Call
_____
Put
_____
Unexpected increase in cash dividends
Call
_____
Put
_____
ANSWER:
Increase in interest rates
Call
Rise
Put
Fall
Decrease in time until expiration
Call
Fall
Put
Fall
Decrease in stock volatility
Call
Fall
Put
Fall
Unexpected increase in cash dividends
Call
Fall
Put
Rise
Short-term interest rates are 5%. An at-the-money six-month $95 call sells for $7. What is the parity value for a six-month at-the-money put, assuming the underlying stock pays no dividends?
ANSWER:
P = C – S + K/(1+R)T = 7 – 95 + 95/(1.05).5 = $4.71
One-year interest rates are 5%. A stock currently sells for $40 and will either rise to $50 or fall to $35 in six months. Using the binomial option pricing model, determine the fair value of a $45 call.
ANSWER:
$50
11430002222500 50 – 5N = 35 N = 3
(40 – 3C)(1.05).5 = 35
115633510350500$40 C = $1.95
$35
6 months
Your company owns coastal land worth $1 million. Pending the outcome of a regulatory decision, in six months the land will either increase in value by exactly 60% or remain unchanged in value. A real estate speculator offers your firm $50,000 for the right to buy the land anytime within the next six months for $1.3 million. The interest rate is 8% per year.
Evaluate this offer and recommend whether or not your company should accept it.
ANSWER:
16135358953500 $1.6 million
16668759842500 $1 million $1 million
1.6 – 0.3N = 1.0 N =2
($1 million – 2C)(1.04) = $1 million
C = $19,231, less than the amount offered. Accept the offer.
A $50, one-year call sells for $4; a $50 one-year put sells for $6.45. If the one-year interest rate is 8%, calculate the implied stock price.
ANSWER:
S = C – P + K/(1+R)T
= 4 – 6.45 + 50/(1.08) = $43.85
Suppose one-year interest rates are 6%. A stock currently sells for $100 and at the end of one year will sell for either $110 or $95.
Using binomial pricing, calculate the value of a $105 call.
Using your answer to part a and the theory of put call parity, calculate the value of a $105 put.
ANSWER:
123253515557500a.
110 110 – 5N = 95
N = 3
123825016510000 (100 – 3C)(1.06) = 95
100 C = $3.46
95
b. P = C – S +K/(1+R)T = 3.46 – 100 + 105/(1.06) = $2.52
