Deck 16: Option Valuation

Question 1

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

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

Answer 1

B

Question 2

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 2

D

Question 3

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

Answer 3

B

Question 4

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 5

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 6

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 7

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

A) the stock price minus the exercise price
B) the exercise 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 8

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

Question 9

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 10

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 11

A 45 put option on a stock priced at $50 is priced at $3.50.This call has an intrinsic value of ______ and a time value of _____.

A) $3.50; $0
B) $5.00; $3.50
C) $3.50; $5.00
D) $0; $3.50

Question 12

The percentage change in the stock 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 13

A 45 call option on a stock priced at $50 is priced at $6.50.This call has an intrinsic value of ______ and a time value of _____.

A) $6.50; $0
B) $5.00; $1.50
C) $1.50; $5.00
D) $0; $6.50

Question 14

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 15

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

Question 16

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 17

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

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

Question 18

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 19

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 20

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 21

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 22

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 23

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 24

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 25

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 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

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 28

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 29

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 30

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 31

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 32

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 33

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 34

Hedge ratios for long calls are always __________.

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

Question 35

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 36

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 37

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 38

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 39

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 one percent change in the value of the underlying asset
D) the percentage change in the value of the underlying asset for a one percent change in the value of the call

Question 40

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 ____________.

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

Question 41

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 42

The current stock price of Johnson and Johnson is $64 and the stock does not pay dividends. The instantaneous risk free rate of return is 5%. The instantaneous standard deviation of J&J's stock is 20%. You wish 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 43

The current stock price of International Paper is $69 and the stock does not pay dividends. The instantaneous risk free rate of return is 10%. The instantaneous standard deviation of International Paper's stock is 25%. You wish 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 44

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 45

The current stock price of Johnson and Johnson is $64 and the stock does not pay dividends. The instantaneous risk free rate of return is 5%. The instantaneous standard deviation of J&J's stock is 20%. You wish to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now.
The stock price of Ajax 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 one year from now should be worth __________ today.

A) $11.59
B) $15.00
C) $20.00
D) $40.00

Question 46

The current stock price of International Paper is $69 and the stock does not pay dividends. The instantaneous risk free rate of return is 10%. The instantaneous standard deviation of International Paper's stock is 25%. You wish 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 put option should be worth __________ today.

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

Question 47

The current stock price of Johnson and Johnson is $64 and the stock does not pay dividends. The instantaneous risk free rate of return is 5%. The instantaneous standard deviation of J&J's stock is 20%. You wish 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 put option should be worth __________ today.

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

Question 48

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 49

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 50

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

A) between zero and -1
B) between -1 and 1
C) positive but less than 1
D) greater than 1

Question 51

The current stock price of Alcoa is $70 and the stock does not pay dividends.The instantaneous risk free rate of return is 6%.The instantaneous standard deviation of Alcoa's stock is 40%.You wish 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) .28
B) .31
C) .62
D) .70

Question 52

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

A) long .70 calls for each short stock
B) long .70 shares for each long call
C) long .70 shares for each short call
D) short .70 calls for each long stock

Question 53

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 54

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 55

The current stock price of Alcoa is $70 and the stock does not pay dividends.The instantaneous risk free rate of return is 6%.The instantaneous standard deviation of Alcoa's stock is 40%.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 56

The current stock price of Johnson and Johnson is $64 and the stock does not pay dividends. The instantaneous risk free rate of return is 5%. The instantaneous standard deviation of J&J's stock is 20%. You wish to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now.
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 at is 6%.Using the binomial OPM,the value of a put option with an exercise price of $135 and an expiration date one year from now should be worth __________ today.

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

Question 57

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 58

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 59

Hedge ratios for long call position are __________ and hedge ratios for long put positions are ____________.

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

Question 60

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 mis-pricing situation you may wish 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 write the 105 call
D) write the 105 call and write either the 95 or the 100 call

Question 61

What would have been the cost of a protective put portfolio?

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

Question 62

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 63

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 64

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 65

You would like to be holding 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) -1.0
B) -0.5
C) 0.5
D) 1.0

Question 66

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) $2.04
D) $2.19

Question 67

The intrinsic value of an out of the money call option ___________.

A) is negative
B) is positive
C) is zero
D) can not be determined

Question 68

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 69

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 = 3.0%.Standard deviation = 35%.

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

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

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 72

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 73

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 74

A call option on Juniper Corp.stock with an exercise price of $75 and an expiration date one year from now is worth $3.00 today.A put option on Juniper Corp.stock with an exercise price of $75 and an expiration date one 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 75

You would like to be holding 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) $5.00
D) $3.33

Question 76

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) $0.00
B) $1.25
C) $4.00
D) $5.25

Question 77

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 78

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) $0.00
B) $0.75
C) $1.50
D) $2.25

Question 79

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 six months from now is worth $5.00 today.A put option on Atlantis Corp.stock with an exercise price of $40 and an expiration date six months from now should be worth __________ today.

A) $0.05
B) $0.14
C) $2.00
D) $3.95

Question 80

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