Deck 16: Option Valuation

Question 1

A call option with several months until expiration has a strike price of $55 when the stock price is $50. The option has ________ intrinsic value and ________ time value.

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

Answer 1

D

Question 2

The value of a call option increases with all of the following except ________.

A) stock price
B) time to maturity
C) volatility
D) dividend yield

Answer 2

D

Question 3

Investor A bought a call option, and investor B bought a put option. All else equal, if the interest rate increases, the value of investor A's position will ________ and the value of investor B's position will ________.

A) increase; increase
B) increase; decrease
C) decrease; increase
D) decrease; decrease

Answer 3

B

Question 4

A stock with a current market price of $50 and a strike price of $45 has an associated call option priced at $6.50. This call has an intrinsic value of ________ and a time value of ________.

A) $5; $1.50
B) $1.50; $5
C) $0; $6.50
D) $6.50; $0

Question 5

The Black-Scholes option-pricing formula was developed for ________.

A) American options
B) European options
C) Tokyo options
D) out-of-the-money options

Question 6

Investor A bought a call option that expires in 6 months. Investor B wrote a put option with a 9-month maturity. All else equal, as the time to expiration approaches, the value of investor A's position will ________ and the value of investor B's position will ________.

A) increase; increase
B) increase; decrease
C) decrease; increase
D) decrease; decrease

Question 7

A stock with a current market price of $50 and a strike price of $45 has an associated put option priced at $3.50. This put has an intrinsic value of ________ and a time value of ________.

A) $3.50; $0
B) $5; $3.50
C) $3.50; $5
D) $0; $3.50

Question 8

The percentage change in the call option price divided by the percentage change in the stock price is the ________ of the option.

A) delta
B) elasticity
C) gamma
D) theta

Question 9

All else equal, call option values are ________ if the ________ is lower.

A) higher; stock price
B) higher; exercise price
C) lower; dividend payout
D) higher; lower volatility

Question 10

A put option with several months until expiration has a strike price of $55 when the stock price is $50. The option has ________ intrinsic value and ________ time value.

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

Question 11

The intrinsic value of a call option is equal to ________.

A) the stock price minus the exercise price
B) the exercise price minus the stock price
C) the stock price minus the exercise price plus any expected dividends
D) the exercise price minus the stock price plus any expected dividends

Question 12

Before expiration, the time value of an out-of-the-money stock option is ________.

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

Question 13

The ________ is the stock price minus exercise price, or the profit that could be attained by immediate exercise of an in-the-money call option.

A) intrinsic value
B) time value
C) stated value
D) discounted value

Question 14

The value of a put option increases with all of the following except ________.

A) stock price
B) time to maturity
C) volatility
D) dividend yield

Question 15

If the Black-Scholes formula is solved to find the standard deviation consistent with the current market call premium, that standard deviation would be called the ________.

A) variability
B) volatility
C) implied volatility
D) deviance

Question 16

Investor A bought a call option, and investor B bought a put option. All else equal, if the underlying stock price volatility increases, the value of investor A's position will ________ and the value of investor B's position will ________.

A) increase; increase
B) increase; decrease
C) decrease; increase
D) decrease; decrease

Question 17

The hedge ratio is often called the option's ________.

A) delta
B) gamma
C) theta
D) beta

Question 18

A ________ is an option valuation model based on the assumption that stock prices can move to only two values over any short time period.

A) nominal model
B) binomial model
C) time model
D) Black-Scholes model

Question 19

The ________ is the difference between the actual call price and the intrinsic value.

A) stated value
B) strike value
C) time value
D) binomial value

Question 20

The divergence between an option's intrinsic value and its market value is usually greatest when ________.

A) the option is deep in the money
B) the option is approximately at the money
C) the option is far out of the money
D) time to expiration is very low

Question 21

Which of the following is a true statement?

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

Question 22

In the Black-Scholes model, as the stock's price increases, the values of N(d1) and N(d2) will ________ for a call and ________ for a put option.

A) increase; decrease
B) increase; increase
C) decrease; increase
D) decrease; decrease

Question 23

The Black-Scholes hedge ratio for a long put option is equal to ________.

A) N(d1)
B) N(d2)
C) N(d1) − 1
D) N(d2) − 1

Question 24

In a binomial option model with three subintervals, the probability that the stock price moves up every possible time is ________.

A) 25%
B) 15.5%
C) 12.5%
D) 8%

Question 25

According to the Black-Scholes option-pricing model, two options on the same stock but with different exercise prices should always have the same ________.

A) price
B) expected return
C) implied volatility
D) maximum loss

Question 26

Strike prices of options are adjusted for ________ but not for ________.

A) dividends; stock splits
B) stock splits; cash dividends
C) exercise of warrants; stock splits
D) stock price movements; stock dividends

Question 27

Of the variables in the Black-Scholes OPM, the ________ is not directly observable.

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

Question 28

A high dividend payout will ________ the value of a call option and ________ the value of a put option.

A) increase; decrease
B) increase; increase
C) decrease; increase
D) decrease; decrease

Question 29

The Black-Scholes hedge ratio for a long call option is equal to ________.

A) N(d1)
B) N(d2)
C) N(d1) − 1
D) N(d2) − 1

Question 30

Research suggests that option-pricing models that allow for the possibility of ________ provide more accurate pricing than does the basic Black-Scholes option-pricing model.
I) early exercise
II) changing expected returns of the stock
III) time varying stock price volatility

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

Question 31

Perfect dynamic hedging requires ________.

A) a smaller capital outlay than static hedging
B) less commission expense than static hedging
C) daily rebalancing
D) continuous rebalancing

Question 32

Research suggests that the performance of the Black-Scholes option-pricing model has ________.

A) improved in recent years
B) remained about the same over time
C) been deficient for stocks with high dividend payouts
D) varied widely over the years since 1973

Question 33

Research conducted by Rubinstein (1994) suggests that ________ command a disproportionately high time value.

A) out-of-the-money call options
B) out-of-the-money put options
C) in-the-money call options
D) in-the-money put options

Question 34

In the Black-Scholes model, if an option is not likely to be exercised, both N(d1) and N(d2) will be close to ________. If the option is definitely likely to be exercised, N(d1) and N(d2) will be close to ________.

A) 1; 0
B) 0; 1
C) −1; 1
D) 1; −1

Question 35

Hedge ratios for long calls are always ________.

A) between −1 and 0
B) between 0 and 1
C) 1
D) greater than 1

Question 36

The delta of an option is ________.

A) the change in the dollar value of an option for a dollar change in the price of the underlying asset
B) the change in the dollar 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 percentage change in the value of the underlying asset for a 1% change in the value of the call

Question 37

When the returns of an option and stock are perfectly correlated as in a two-state binomial option model, the hedge ratio must be equal to the ratio of ________.

A) the range of the option outcomes to the range of the stock outcomes
B) the range of the stock outcomes to the range of the option outcomes
C) the standard deviation of the option returns to the standard deviation of the stock returns
D) the standard deviation of the stock returns to the standard deviation of the option returns

Question 38

The practice of using options or dynamic hedging strategies to provide protection against investment losses while maintaining upside potential is called ________.

A) trading on gamma
B) index optioning
C) portfolio insurance
D) index arbitrage

Question 39

If you know that a call option will be profitably exercised, then the Black-Scholes model price will simplify to ________.

A) S0 − X
B) X − S0
C) S0 − PV(X)
D) PV(X) − S0

Question 40

A longer time to maturity will unambiguously increase the value of a call option because:
I) The longer maturity time reduces the effect of a dividend on call price.
II) With a longer time to maturity the present value of the exercise price falls.
III) With a longer time to maturity the range of possible stock prices at expiration increases.

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

Question 41

The current stock price of National Paper is $69, and the stock does not pay dividends. The instantaneous risk-free rate of return is 10%. The instantaneous standard deviation of National Paper's stock is 25%. You want to purchase a call option on this stock with an exercise price of $70 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the call option should be worth ________ today.

A) $2.50
B) $2.94
C) $3.26
D) $3.50

Question 42

The current stock price of National Paper is $69, and the stock does not pay dividends. The instantaneous risk-free rate of return is 10%. The instantaneous standard deviation of National Paper's stock is 25%. You want to purchase a put option on this stock with an exercise price of $70 and an expiration date 73 days from now.
Using the Black-Scholes, the put option should be worth ________ today.

A) $1.50
B) $2.88
C) $2.55
D) $3.00

Question 43

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

A) long 0.70 calls for each short stock
B) long 0.70 shares for each long call
C) long 0.70 shares for each short call
D) short 0.70 calls for each long stock

Question 44

The delta of a call option on a stock is always ________.

A) negative and less than −1
B) between −1 and 1
C) positive
D) positive but less than 1

Question 45

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a put option on this stock with an exercise price of $55 and an expiration date 73 days from now.
Using Black-Scholes, the put option should be worth ________ today.

A) $0.01
B) $0.07
C) $9.26
D) $9.62

Question 46

You are considering purchasing a call option with a strike price of $35. The price of the underlying stock is currently $27. Without any further information, you would expect the hedge ratio for this option to be ________.

A) negative and near 0
B) negative and near −1
C) positive and near 0
D) positive and near 1

Question 47

You find the option prices for three June call options on the same stock. The 95 call has an implied volatility of 25%, the 100 call has an implied volatility of 25%, and the 105 call has an implied volatility of 30%. If you believe this represents a mispricing situation. you may want to ________.

A) buy the 105 call and write the 100 call
B) buy the 105 call and write the 95 call
C) buy either the 95 or the 100 call and write the 105 call
D) write the 105 call and write either the 95 or the 100 call

Question 48

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now.
Using the Black-Scholes OPM, the call option should be worth ________ today.

A) $0.01
B) $0.08
C) $9.26
D) $9.62

Question 49

If you have an extremely "bullish" outlook on the stock market, you could attempt to maximize your rate of return by ________.

A) purchasing out-of-the-money call options
B) purchasing at-the-money bull spreads
C) purchasing in-the-money call options
D) purchasing at-the-money call options

Question 50

Which one of the following will increase the value of a put option?

A) a decrease in the exercise price
B) a decrease in time to expiration of the put
C) an increase in the volatility of the underlying stock
D) an increase in stock price

Question 51

The delta of a put option on a stock is always ________.

A) between 0 and −1
B) between −1 and 1
C) positive but less than 1
D) greater than 1

Question 52

The stock price of Bravo Corp. is currently $100. The stock price a year from now will be either $160 or $60 with equal probabilities. The interest rate at which investors invest in riskless assets is 6%. Using the binomial OPM, the value of a put option with an exercise price of $135 and an expiration date 1 year from now should be worth ________ today.

A) $34.09
B) $37.50
C) $38.21
D) $45.45

Question 53

The stock price of Apax Inc. is currently $105. The stock price a year from now will be either $130 or $90 with equal probabilities. The interest rate at which investors can borrow is 10%. Using the binomial OPM, the value of a call option with an exercise price of $110 and an expiration date 1 year from now should be worth ________ today.

A) $11.59
B) $15
C) $20
D) $40

Question 54

The price of a stock put option is ________ correlated with the stock price and ________ correlated with the exercise price.

A) negatively; negatively
B) negatively; positively
C) positively; negatively
D) positively; positively

Question 55

If a stock price increases, the price of a put option on the stock will ________ and the price of a call option on the stock will ________.

A) decrease; decrease
B) decrease; increase
C) increase; decrease
D) increase; increase

Question 56

Hedge ratios for long call positions are ________, and hedge ratios for long put positions are ________.

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

Question 57

A higher-dividend payout policy will have a ________ impact on the value of a put and a ________ impact on the value of a call.

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

Question 58

The current stock price of Alcoco is $70, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoco's stock is 40%. You want to purchase a put option on this stock with an exercise price of $75 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold ________ shares of stock per 100 put options to hedge your risk.

A) 30
B) 34
C) 69
D) 74

Question 59

A one-dollar increase in a stock's price would result in ________ in the call option's value of ________ than one dollar.

A) a decrease; less
B) a decrease; more
C) an increase; less
D) an increase; more

Question 60

The current stock price of Alcoco is $70, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoco's stock is 40%. You want to purchase a call option on this stock with an exercise price of $75 and an expiration date 30 days from now. Based on the Black-Scholes OPM, the call option's delta will be ________.

A) 0.28
B) 0.31
C) 0.62
D) 0.70

Question 61

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
Suppose the desired put options with X = 50 were traded. How much would it cost to purchase?

A) $1.19
B) $2.38
C) $5
D) $3.33

Question 62

A call option on Juniper Corp. stock with an exercise price of $75 and an expiration date 1 year from now is worth $3 today. A put option on Juniper Corp. stock with an exercise price of $75 and an expiration date 1 year from now is worth $2.50 today. The risk-free rate of return is 8%, and Juniper Corp. pays no dividends. The stock should be worth ________ today.

A) $69.73
B) $71.69
C) $73.12
D) $77.25

Question 63

A call option has an exercise price of $35 and a stock price of $36.50. If the call option is trading at $2.25, what is the time value embedded in the option?

A) $0
B) $0.75
C) $1.50
D) $2.25

Question 64

The time value of a call option is likely to decline most rapidly ________ days before expiration?

A) 10
B) 30
C) 60
D) 90

Question 65

A call option has an exercise price of $30 and a stock price of $34. If the call option is trading for $5.25, what is the intrinsic value of the option?

A) $0
B) $1.25
C) $4
D) $5.25

Question 66

The stock price of Harper Corp. is $33 today. The risk-free rate of return is 6%, and Harper Corp. pays no dividends. A put option on Harper Corp. stock with an exercise price of $30 and an expiration date 73 days from now is worth $0.95 today. A call option on Harper Corp. stock with an exercise price of $30 and the same expiration date should be worth ________ today.

A) $2.25
B) $3.14
C) $3.99
D) $4.31

Question 67

The fact that American put values may not equal the price implied by put-call parity is attributable to the possibility of what event?

A) changes in the dividend
B) early exercise
C) interest rate declines
D) interest rate rises

Question 68

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
What would have been the cost of a protective put portfolio?

A) $48.81
B) $51.19
C) $52.38
D) $53.38

Question 69

You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay dividends, but the actual call price is $3.75. The most likely explanation for the discrepancy is that either the option is ________ or the volatility you input into the model is too ________.

A) overvalued and should be written; low
B) undervalued and should be written; low
C) overvalued and should be purchased; high
D) undervalued and should be purchased; high

Question 70

You are considering purchasing a put option on a stock with a current price of $33. The exercise price is $35, and the price of the corresponding call option is $2.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be ________.

A) $2.25
B) $3.91
C) $4.05
D) $5.52

Question 71

According to the put-call parity theorem, the payoffs associated with ownership of a call option can be replicated by ________.

A) shorting the underlying stock, borrowing the present value of the exercise price, and writing a put on the same underlying stock and with the same exercise price
B) buying the underlying stock, borrowing the present value of the exercise price, and buying a put on the same underlying stock and with the same exercise price
C) buying the underlying stock, borrowing the present value of the exercise price, and writing a put on the same underlying stock and with the same exercise price
D) shorting the underlying stock, lending the present value of the exercise price, and buying a put on the same underlying stock and with the same exercise price

Question 72

Calculate the price of a call option using the Black Scholes model and the following data: stock price = $47.30, exercise price = $50, time to expiration = 85 days, risk-free rate = 3%, standard deviation = 35%.

A) $1.11
B) $2.22
C) $3.33
D) $4.44

Question 73

The stock price of Atlantis Corp. is $43 today. The risk-free rate of return is 10%, and Atlantis Corp. pays no dividends. A call option on Atlantis Corp. stock with an exercise price of $40 and an expiration date 6 months from now is worth $5 today. A put option on Atlantis Corp. stock with an exercise price of $40 and an expiration date 6 months from now should be worth ________ today.

A) $0.05
B) $0.14
C) $2
D) $3.95

Question 74

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = $50?

A) ½ share of stock and $25 in bills
B) 1 share of stock and $50 in bills
C) ½ share of stock and $26.19 in bills
D) 1 share of stock and $25 in bills

Question 75

The intrinsic value of an out-of-the-money call option ________.

A) is negative
B) is positive
C) is zero
D) cannot be determined

Question 76

Suppose you purchase a call and write a put on the same stock with the same exercise price and expiration. If prices are at equilibrium, the value of this portfolio is ________.

A) S0 − Xe−rt
B) S0 − X
C) S0 + Xe−rt
D) S0 + X

Question 77

What aspect of the time value of money does the factor of e represent in the Black-Scholes option value formula?

A) annual compounding
B) compounding at the expiration time frame
C) continuous compounding
D) daily compounding

Question 78

What combination of variables is likely to lead to the lowest time value?

A) short time to expiration and low volatility
B) long time to expiration and high volatility
C) short time to expiration and high volatility
D) long time to expiration and low volatility

Question 79

Calculate the price of a European call option using the Black Scholes model and the following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%.

A) $1.49
B) $1.79
C) $2.19
D) $2.29

Question 80

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
Suppose the desired put options with X = 50 were traded. What would be the hedge ratio for the option?

A) −1
B) −0.5
C) 0.5
D) 1