Deck 3: Principles of Option Pricing

Question 1

If there are no dividends on a stock,which of the following statements is correct?

A)An American call will sell for more than a European call
B)A European call will sell for more than an American call
C)An American call will be immediately exercised
D)An American call and an American put will sell for the same price
E)none of the above

Answer 1

E

Question 2

Suppose you use put-call parity to compute a European call price from the European put price,the stock price,and the risk-free rate.You find the market price of the call to be less than the price given by put-call parity.Ignoring transaction costs,what trades should you do?

A)buy the call and the risk-free bonds and sell the put and the stock
B)buy the stock and the risk-free bonds and sell the put and the call
C)buy the put and the stock and sell the risk-free bonds and the call
D)buy the put and the call and sell the risk-free bonds and the stock
E)none of the above

Answer 2

A

Question 3

What is the lowest possible value of a European put?

A)Max(0,X - S₀)
B)X(1 + r)^-T
C)Max[0,S₀ - X(1 + r)^-T]
D)Max[0,X(1 + r)^-T - S₀)]
E)none of the above

Answer 3

D

Question 4

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the time value of the December 105 put?

A)1.30
B)8.30
C)0.00
D)7.00
E)none of the above

Question 5

Suppose the stock is about to go ex-dividend in one day.The dividend will be $4.00.Which of the following calls will you consider for exercise?

A)November 115
B)November 110
C)December 115
D)all of the above
E)none of the above

Question 6

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the European lower bound of the December 105 call?

A)9.86
B)0.00
C)8.25
D)9.26
E)none of the above

Question 7

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the intrinsic value of the January 110 call?

A)0.00
B)8.30
C)3.75
D)5.00
E)none of the above

Question 8

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the intrinsic value of the December 115 put?

A)1.75
B)0.00
C)3.90
D)3.00
E)none of the above

Question 9

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the time value of the November 115 put?

A)1.75
B)2.80
C)1.10
D)0.00
E)none of the above

Question 10

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the European lower bound of the November 115 call?

A)1.44
B)0.00
C)1.75
D)2.06
E)none of the above

Question 11

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the intrinsic value of the November 105 put?

A)0.30
B)8.25
C)8.50
D)0.00
E)none of the above

Question 12

Consider a portfolio consisting of a long call with an exercise price of X,a short position in a non-dividend paying stock at an initial price of S₀,and the purchase of riskless bonds with a face value of X and maturing when the call expires.What should such a portfolio be worth?

A)C + P - X(1 + r)^-T
B)C - S₀
C)P - X
D)P + S₀ - X(1 + r)^-T
E)none of the above

Question 13

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the time value of the November 110 call?

A)0.00
B)4.40
C)1.15
D)3.25
E)none of the above

Question 14

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the intrinsic value of the November 115 call?

A)1.50
B)0.00
C)2.80
D)1.75
E)none of the above

Question 15

Another expression for intrinsic value is

A)parity
B)parity value
C)exercise value
D)all of the above
E)none of the above

Question 16

Suppose you knew that the January 115 options were correctly priced but suspected that the stock was mispriced.Using put-call parity,what would you expect the stock price to be? For this problem,treat the options as if they were European.

A)113.73
B)123.23
C)121.23
D)112.77
E)none of the above

Question 17

The maximum difference between the January 105 and 110 calls is which of the following?

A)11.50
B)4.92
C)5.00
D)4.0
E)none of the above

Question 18

From American put-call parity,what are the minimum and maximum values that the sum of the stock price and December 110 put price can be?

A)101.81 and 102.87
B)2.50 and 113.25
C)116.038 and 117.10
D)7.125 and 110
E)none of the above

Question 19

On March 2,a Treasury bill expiring on April 20 had a bid discount of 5.80,and an ask discount of 5.86.What is the best estimate of the risk-free rate as given in the text?

A)5.86 %
B)5.83 %
C)6.11 %
D)6.14 %
E)none of the above

Question 20

The following quotes were observed for options on a given stock on November 1 of a given year.These are American calls except where indicated.Use the information to answer questions 7 through 20.
The stock price was 113.25.The risk-free rates were 7.30 percent (November),7.50 percent (December)and 7.62 percent (January).The times to expiration were 0.0384 (November),0.1342 (December),and 0.211 (January).Assume no dividends unless indicated.
What is the time value of the January 115 call?

A)5.30
B)0.00
C)3.50
D)1.70
E)none of the above

Question 21

The lower bound of a European call on a non-dividend paying stock is lower than the intrinsic value of an American call.

Question 22

The lower the exercise price,the more valuable the call option.

Question 23

If one portfolio always provides a return at least as high as another portfolio,then that portfolio will have a price no less than that of the other portfolio.

Question 24

Holding everything else constant,call options are more expensive in periods of high interest rates.

Question 25

The maximum value of a call is the stock price.

Question 26

An American put might be exercised early even when there are no dividends on the underlying stock.

Question 27

Which of the following is the lowest possible value of an American put on a stock with no dividends?

A)X(1 + r)^-T
B)X
C)Max(0,X(1 + r)^-T - S₀)
D)Max(0,X - S₀)
E)none of the above

Question 28

Holding everything else constant,put options are more expensive in periods of high interest rates.

Question 29

Holding everything else constant,a longer-term European put is always worth more than a shorter-term European put.

Question 30

The difference between a Treasury bill's face value and its price is called the

A)time value
B)discount
C)coupon rate
D)bid
E)none of the above

Question 31

Which of the following is the lowest possible value of an American call on a stock with no dividends?

A)Max(0,S₀ - X(1 + r)^-T)
B)S₀
C)Max(0,S₀ - X)
D)Max(0,S₀ (1 + r)^-T - X)
E)none of the above

Question 32

An option can be priced at less than zero because it can potentially generate a large profit for its owner.

Question 33

High volatility is bad for option holders because it increases the probability that the option will expire out-of-the-money.

Question 34

The time value of an option is also referred to as the

A)synthetic value
B)strike value
C)speculative value
D)parity value
E)none of the above

Question 35

The difference between an American call's price and its intrinsic value is called the time value because the call can be exercised at any time.

Question 36

Which of the following statements about an American call is not true?

A)Its time value decreases as expiration approaches
B)Its maximum value is the stock price
C)It can be exercised prior to expiration
D)It pays dividends
E)none of the above

Question 37

Put-call parity is a relationship that can be used to provide the price of both a European put and call simultaneously.

Question 38

The lower bound of a European put on a non-dividend paying stock is lower than the intrinsic value of an American put.

Question 39

An American call should be exercised early when the stock price is extremely high and is expected to fall.

Question 40

The concept of the intrinsic value does not apply to European calls prior to expiration because they cannot be exercised immediately.

Question 41

The time value of a call is greatest when the stock price is very high.

Question 42

The spread between the prices of two European puts,alike in all respects except exercise price,cannot exceed the difference in their exercise prices.

Question 43

A stock is equivalent to a long call,short put and long risk-free bond.

Question 44

At expiration the call price must converge to the stock price.

Question 45

An American call on a non-dividend paying stock will be worth more than a European call on that same stock.

Question 46

The gain from the early exercise of an American put is X(1 + r)^-T - S₀.

Question 47

Selling short a risk-free bond is equivalent to borrowing.

Question 48

If an option portfolio generates a zero cash flow at expiration and a positive cash flow today,an arbitrage opportunity is available.

Question 49

Even if there are no dividends on the stock,American put-call parity will not be the same as European put-call parity.

Question 50

Transactions to exploit pricing errors in the put-call parity relationship are called conversions and reversals.