Deck 21: Option Valuation

Question 1

At expiration, the time value of an in-the-money put option is always

A) equal to zero.
B) negative.
C) positive.
D) equal to the stock price minus the exercise price.
E) None of the options are correct.

Answer 1

A
Explanation: The difference between the actual option price and the intrinsic value is called the time value of the option. Time value is always zero at expiration.

Question 2

Prior to expiration,

A) the intrinsic value of a call option is greater than its actual value.
B) the intrinsic value of a call option is always positive.
C) the actual value of a call option is greater than the intrinsic value.
D) the intrinsic value of a call option is always greater than its time value.

Answer 2

C
Explanation: Prior to expiration, any option will be selling for a positive price, thus the actual value is usually greater than the intrinsic value.

Question 3

Other things equal, the price of a stock call option is negatively correlated with which of the following factors?

A) The stock price
B) The time to expiration
C) The stock volatility
D) The exercise price
E) The stock price, time to expiration, and stock volatility

Answer 3

D
Explanation: The exercise price is negatively correlated with the call option price.

Question 4

Other things equal, the price of a stock call option is positively correlated with which of the following factors?

A) The stock price
B) The time to expiration
C) The stock volatility
D) The exercise price
E) The stock price, time to expiration, and stock volatility

Question 5

Before expiration, the time value of an in-the-money put option is always

A) equal to zero.
B) negative.
C) positive.
D) equal to the stock price minus the exercise price.
E) None of the options are correct.

Question 6

Other things equal, the price of a stock call option is positively correlated with the following factors except

A) the stock price.
B) the time to expiration.
C) the stock volatility.
D) the exercise price.

Question 7

Prior to expiration,

A) the intrinsic value of a put option is greater than its actual value.
B) the intrinsic value of a put option is always positive.
C) the actual value of a put option is greater than the intrinsic value.
D) the intrinsic value of a put option is always greater than its time value.

Question 8

Before expiration, the time value of an at-the-money call option is usually

A) positive.
B) equal to zero.
C) negative.
D) equal to the stock price minus the exercise price.
E) None of the options are correct.

Question 9

At expiration, the time value of an at-the-money put option is always

A) equal to zero.
B) equal to the stock price minus the exercise price.
C) negative.
D) positive.

Question 10

A call option has an intrinsic value of zero if the option is

A) at the money.
B) out of the money.
C) in the money.
D) at the money and in the money.
E) at the money or out of the money.

Question 11

At expiration, the time value of an in-the-money call option is always

A) equal to zero.
B) positive.
C) negative.
D) equal to the stock price minus the exercise price.
E) None of the options are correct.

Question 12

A put option has an intrinsic value of zero if the option is

A) at the money.
B) out of the money.
C) in the money.
D) at the money and in the money.
E) at the money or out of the money.

Question 13

At expiration, the time value of an at-the-money call option is always

A) positive.
B) equal to zero.
C) negative.
D) equal to the stock price minus the exercise price.

Question 14

If the stock price decreases, the price of a put option on that stock __________, and that of a call option __________.

A) decreases; increases
B) decreases; decreases
C) increases; decreases
D) increases; increases
E) does not change; does not change

Question 15

Before expiration, the time value of an in-the-money call option is always

A) equal to zero.
B) positive.
C) negative.
D) equal to the stock price minus the exercise price.
E) None of the options are correct.

Question 16

If the stock price increases, the price of a put option on that stock __________, and that of a call option __________.

A) decreases; increases
B) decreases; decreases
C) increases; decreases
D) increases; increases
E) does not change; does not change

Question 17

Other things equal, the price of a stock put option is positively correlated with which of the following factors?

A) The stock price
B) The time to expiration
C) The stock volatility
D) The exercise price
E) The time to expiration, stock volatility, and exercise price

Question 18

Other things equal, the price of a stock put option is positively correlated with the following factors except

A) the stock price.
B) the time to expiration.
C) the stock volatility.
D) the exercise price.

Question 19

Other things equal, the price of a stock put option is negatively correlated with which of the following factors?

A) The stock price
B) The time to expiration
C) The stock volatility
D) The exercise price
E) The time to expiration, stock volatility, and exercise price

Question 20

Before expiration, the time value of an at-the-money put option is always

A) equal to zero.
B) equal to the stock price minus the exercise price.
C) negative.
D) positive.
E) None of the options are correct.

Question 21

The dollar change in the value of a stock call option is always

A) lower than the dollar change in the value of the stock.
B) higher than the dollar change in the value of the stock.
C) negatively correlated with the change in the value of the stock.
D) higher than the dollar change in the value of the stock and negatively correlated with the change in the value of the stock.
E) lower than the dollar change in the value of the stock and negatively correlated with the change in the value of the stock.

Question 22

A hedge ratio for a put is always

A) equal to one.
B) greater than one.
C) between zero and one.
D) between negative one and zero.
E) of no restricted value.

Question 23

The price of a stock put option is __________ correlated with the stock price and __________ correlated with the strike price.

A) positively; positively
B) negatively; positively
C) negatively; negatively
D) positively; negatively
E) not; not

Question 24

Which of the inputs in the Black-Scholes option pricing model are directly observable?

A) The price of the underlying security
B) The risk-free rate of interest
C) The time to expiration
D) The variance of returns of the underlying asset return
E) The price of the underlying security, risk-free rate of interest, and time to expiration

Question 25

Delta neutral

A) is the volatility level for the stock that the option price implies.
B) is the continued updating of the hedge ratio as time passes.
C) is the percentage change in the stock call-option price divided by the percentage change in the stock price.
D) means the portfolio has no tendency to change value as the underlying portfolio value changes.

Question 26

The elasticity of a stock put option is always

A) positive.
B) smaller than one.
C) negative.
D) infinite.

Question 27

The price of a stock call option is __________ correlated with the stock price and __________ correlated with the strike price.

A) positively; positively
B) negatively; positively
C) negatively; negatively
D) positively; negatively
E) not; not

Question 28

Portfolio A consists of 150 shares of stock and 300 calls on that stock. Portfolio B consists of 575 shares of stock. The call delta is 0.7. Which portfolio has a higher dollar exposure to a change in stock price?

A) Portfolio B
B) Portfolio A
C) The two portfolios have the same exposure.
D) Portfolio A if the stock price increases and portfolio B if it decreases
E) Portfolio B if the stock price increases and portfolio A if it decreases

Question 29

A hedge ratio for a call option is ________, and a hedge ratio for a put option is ______.

A) negative; positive
B) negative; negative
C) positive; negative
D) positive; positive
E) zero; zero

Question 30

Delta is defined as

A) the change in the value of an option for a dollar change in the price of the underlying asset.
B) the change in the value of the underlying asset for a dollar change in the call price.
C) the percentage change in the value of an option for a 1% change in the value of the underlying asset.
D) the change in the volatility of the underlying stock price.
E) None of the options are correct.

Question 31

Dynamic hedging is

A) the volatility level for the stock that the option price implies.
B) the continued updating of the hedge ratio as time passes.
C) the percentage change in the stock call-option price divided by the percentage change in the stock price.
D) the sensitivity of the delta to the stock price.

Question 32

The gamma of an option is

A) the volatility level for the stock that the option price implies.
B) the continued updating of the hedge ratio as time passes.
C) the percentage change in the stock call-option price divided by the percentage change in the stock price.
D) the sensitivity of the delta to the stock price.

Question 33

The elasticity of a stock call option is always

A) greater than one.
B) smaller than one.
C) negative.
D) infinite.
E) None of the options are correct.

Question 34

A hedge ratio for a call is always

A) equal to one.
B) greater than one.
C) between zero and one.
D) between negative one and zero.
E) of no restricted value.

Question 35

All the inputs in the Black-Scholes option pricing model are directly observable except

A) the price of the underlying security.
B) the risk-free rate of interest.
C) the time to expiration.
D) the variance of returns of the underlying asset return.

Question 36

A hedge ratio of 0.70 implies that a hedged portfolio should consist of

A) long 0.70 calls for each short stock.
B) short 0.70 calls for each long stock.
C) long 0.70 shares for each short call.
D) long 0.70 shares for each long call.
E) None of the options are correct.

Question 37

The percentage change in the stock call-option price divided by the percentage change in the stock price is called

A) the elasticity of the option.
B) the delta of the option.
C) the theta of the option.
D) the gamma of the option.

Question 38

A hedge ratio of 0.85 implies that a hedged portfolio should consist of

A) long 0.85 calls for each short stock.
B) short 0.85 calls for each long stock.
C) long 0.85 shares for each short call.
D) long 0.85 shares for each long call.
E) None of the options are correct.

Question 39

The elasticity of an option is

A) the volatility level for the stock that the option price implies.
B) the continued updating of the hedge ratio as time passes.
C) the percentage change in the stock call-option price divided by the percentage change in the stock price.
D) the sensitivity of the delta to the stock price.

Question 40

Volatility risk is

A) the volatility level for the stock that the option price implies.
B) the risk incurred from unpredictable changes in volatility.
C) the percentage change in the stock call-option price divided by the percentage change in the stock price.
D) the sensitivity of the delta to the stock price.

Question 41

A portfolio consists of 800 shares of stock and 100 calls on that stock. If the hedge ratio for the call is 0.5, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

A) +$700
B) −$850
C) −$580
D) −$520

Question 42

If the hedge ratio for a stock call is 0.30, the hedge ratio for a put with the same expiration date and exercise price as the call would be

A) 0.70.
B) 0.30.
C) −0.70.
D) −0.30.
E) −0.17.

Question 43

A put option on the S&P 500 Index will best protect a portfolio

A) of 100 shares of IBM stock.
B) of 50 bonds.
C) that corresponds to the S&P 500.
D) of 50 shares of AT&T and 50 shares of Xerox stocks.
E) that replicates the Dow.

Question 44

If the hedge ratio for a stock call is 0.70, the hedge ratio for a put with the same expiration date and exercise price as the call would be

A) 0.70.
B) 0.30.
C) −0.70.
D) −0.30.
E) −0.17.

Question 45

Higher dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to lower dividend-payout policies.

A) negative; negative
B) positive; positive
C) positive; negative
D) negative; positive
E) zero; zero

Question 46

If the hedge ratio for a stock call is 0.60, the hedge ratio for a put with the same expiration date and exercise price as the call would be

A) 0.60.
B) 0.40.
C) −0.60.
D) −0.40.
E) −0.17.

Question 47

A portfolio consists of 100 shares of stock and 1500 calls on that stock. If the hedge ratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

A) +$700
B) +$500
C) −$1,150
D) −$520

Question 48

If the hedge ratio for a stock call is 0.50, the hedge ratio for a put with the same expiration date and exercise price as the call would be

A) 0.30.
B) 0.50.
C) −0.60.
D) −0.50.
E) −0.17.

Question 49

A $1 decrease in a call option's exercise price would result in a(n) __________ in the call option's value of __________ one dollar.

A) increase; more than
B) decrease; more than
C) decrease; less than
D) increase; less than
E) increase; exactly

Question 50

Portfolio A consists of 600 shares of stock and 300 calls on that stock. Portfolio B consists of 685 shares of stock. The call delta is 0.3. Which portfolio has a higher dollar exposure to a change in stock price?

A) Portfolio B
B) Portfolio A
C) The two portfolios have the same exposure.
D) Portfolio A if the stock price increases, and portfolio B if it decreases
E) Portfolio B if the stock price increases, and portfolio A if it decreases

Question 51

Lower dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to higher dividend-payout policies.

A) negative; negative
B) positive; positive
C) positive; negative
D) negative; positive
E) zero; zero

Question 52

A put option is currently selling for $6 with an exercise price of $50. If the hedge ratio for the put is 0.30, and the stock is currently selling for $46, what is the elasticity of the put?

A) 2.76
B) 2.30
C) −7.67
D) −2.76
E) −2.30

Question 53

Relative to European puts, otherwise identical American put options

A) are less valuable.
B) are more valuable.
C) are equal in value.
D) will always be exercised earlier.
E) None of the options are correct.

Question 54

A portfolio consists of 400 shares of stock and 200 calls on that stock. If the hedge ratio for the call is 0.6, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

A) +$700
B) +$500
C) −$580
D) −$520

Question 55

Portfolio A consists of 400 shares of stock and 400 calls on that stock. Portfolio B consists of 500 shares of stock. The call delta is 0.5. Which portfolio has a higher dollar exposure to a change in stock price?

A) Portfolio B
B) Portfolio A
C) The two portfolios have the same exposure.
D) Portfolio A if the stock price increases and portfolio B if it decreases
E) Portfolio B if the stock price increases and portfolio A if it decreases

Question 56

Which one of the following variables influences the value of put options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

A) I and IV only
B) II and III only
C) I, II, and IV only
D) I, II, III, and IV
E) I, II, and III only

Question 57

An American call-option buyer on a nondividend-paying stock will

A) always exercise the call as soon as it is in the money.
B) only exercise the call when the stock price exceeds the previous high.
C) never exercise the call early.
D) buy an offsetting put whenever the stock price drops below the strike price.
E) None of the options are correct.

Question 58

Which one of the following variables influences the value of call options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

A) I and IV only
B) II and III only
C) I, II, and IV only
D) I, II, III, and IV
E) I, II, and III only

Question 59

A portfolio consists of 225 shares of stock and 300 calls on that stock. If the hedge ratio for the call is 0.4, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

A) −$345
B) +$500
C) −$580
D) −$520

Question 60

Portfolio A consists of 500 shares of stock and 500 calls on that stock. Portfolio B consists of 800 shares of stock. The call delta is 0.6. Which portfolio has a higher dollar exposure to a change in stock price?

A) Portfolio B
B) Portfolio A
C) The two portfolios have the same exposure.
D) Portfolio A if the stock price increases and portfolio B if it decreases
E) Portfolio B if the stock price increases and portfolio A if it decreases

Question 61

The intrinsic value of an out-of-the-money call option is equal to

A) the call premium.
B) zero.
C) the stock price minus the exercise price.
D) the striking price.

Question 62

The time value of a call option is I) the difference between the option's price and the value it would have if it were expiring immediately.
II) the same as the present value of the option's expected future cash flows.
III) the difference between the option's price and its expected future value.
IV) different from the usual time value of money concept.

A) I
B) I and II
C) II and III
D) II
E) I and IV

Question 63

The intrinsic value of an at-the-money call option is equal to

A) the call premium.
B) zero.
C) the stock price plus the exercise price.
D) the striking price.
E) None of the options are correct.

Question 64

The Black-Scholes formula assumes that I) the risk-free interest rate is constant over the life of the option.
II) the stock price volatility is constant over the life of the option.
III) the expected rate of return on the stock is constant over the life of the option.
IV) there will be no sudden extreme jumps in stock prices.

A) I and II
B) I and III
C) II and II
D) I, II, and IV
E) I, II, III, and IV

Question 65

In volatile markets, dynamic hedging may be difficult to implement because

A) prices move too quickly for effective rebalancing.
B) as volatility increases, historical deltas are too low.
C) price quotes may be delayed so that correct hedge ratios cannot be computed.
D) volatile markets may cause trading halts.
E) All of the options are correct.

Question 66

Rubinstein (1994) observed that the performance of the Black-Scholes model had deteriorated in recent years, and he attributed this to

A) investor fears of another market crash.
B) higher-than-normal dividend payouts.
C) early exercise of American call options.
D) decreases in transaction costs.
E) None of the options are correct.

Question 67

Empirical tests of the Black-Scholes option pricing model

A) show that the model generates values fairly close to the prices at which options trade.
B) show that the model tends to overvalue deep in-the-money calls and undervalue deep out-of-the-money calls.
C) indicate that the mispricing that does occur is due to the possible early exercise of American options on dividend-paying stocks.
D) show that the model generates values fairly close to the prices at which options trade and indicate that the mispricing that does occur is due to the possible early exercise of American options on dividend-paying stocks.
E) All of the options are correct.

Question 68

An American-style call option with six months to maturity has a strike price of $35. The underlying stock now sells for $43. The call premium is $12. What is the intrinsic value of the call?

A) $12
B) $8
C) $0
D) $23

Question 69

The intrinsic value of an at-the-money put option is equal to

A) the stock price minus the exercise price.
B) the put premium.
C) zero.
D) the exercise price minus the stock price.
E) None of the options are correct.

Question 70

Since deltas change as stock values change, portfolio hedge ratios must be constantly updated in active markets. This process is referred to as

A) portfolio insurance.
B) rebalancing.
C) option elasticity.
D) gamma hedging.
E) dynamic hedging.

Question 71

As the underlying stock's price increased, the call option valuation function's slope approaches

A) zero.
B) one.
C) two times the value of the stock.
D) one-half the value of the stock.
E) infinity.

Question 72

An American-style call option with six months to maturity has a strike price of $35. The underlying stock now sells for $43. The call premium is $12. If the option has delta of .5, what is its elasticity?

A) 4.17
B) 2.32
C) 1.79
D) 0.5
E) 1.5

Question 73

The hedge ratio of an option is also called the option's

A) alpha.
B) beta.
C) sigma.
D) delta.
E) rho.

Question 74

An American-style call option with six months to maturity has a strike price of $35. The underlying stock now sells for $43. The call premium is $12. What is the time value of the call?

A) $8
B) $12
C) $0
D) $4
E) Cannot be determined without more information

Question 75

Options sellers who are delta-hedging would most likely

A) sell when markets are falling.
B) buy when markets are rising.
C) sell when markets are falling and buy when markets are rising.
D) sell whether markets are falling or rising.
E) buy whether markets are falling or rising.

Question 76

An American-style call option with six months to maturity has a strike price of $35. The underlying stock now sells for $43. The call premium is $12. If the company unexpectedly announces it will pay its first-ever dividend three months from today, you would expect that

A) the call price would increase.
B) the call price would decrease.
C) the call price would not change.
D) the put price would decrease.
E) the put price would not change.

Question 77

Use the two-state put-option value in this problem. S_O = $100; X = $120; the two possibilities for S_T are $150 and $80. The range of P across the two states is _____, and the hedge ratio is _______.

A) $0 and $40; −4/7
B) $0 and $50; +4/7
C) $0 and $40; +4/7
D) $0 and $50; −4/7
E) $20 and $40; +1/2

Question 78

The intrinsic value of an in-of-the-money call option is equal to

A) the call premium.
B) zero.
C) the stock price minus the exercise price.
D) the striking price.
E) None of the options are correct.

Question 79

The time value of a put option is I) the difference between the option's price and the value it would have if it were expiring immediately.
II) the same as the present value of the option's expected future cash flows.
III) the difference between the option's price and its expected future value.
IV) different from the usual time value of money concept.

A) I
B) I and II
C) II and III
D) II
E) I and IV

Question 80

The intrinsic value of an in-the-money put option is equal to

A) the stock price minus the exercise price.
B) the put premium.
C) zero.
D) the exercise price minus the stock price.
E) None of the options are correct.