Deck 21: Valuing Options

Question 1

Suppose ACC's stock price is currently $25.In the next six months it will either fall to $15 or rise to $40.What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5% per six-month period.[Use the replicating portfolio method.]

A)$20.00
B)$8.57
C)$9.52
D)$13.10

Answer 1

$8.57

Question 2

What does an equity option's delta reflect?

A)The volatility of the underlying stock price
B)The dividends paid to the underlying stockholders
C)The number of shares needed to replicate one call option
D)The time to expiration

Answer 2

The number of shares needed to replicate one call option

Question 3

Relative to the underlying stock,a call option always has:

A)a higher beta and a higher standard deviation of return.
B)a lower beta and a higher standard deviation of return.
C)a higher beta and a lower standard deviation of return.
D)a lower beta and a lower standard deviation of return.

Answer 3

a higher beta and a higher standard deviation of return.

Question 4

Suppose Carol's stock price is currently $20.In each six-month period it will either fall by 50% or rise by 100%.What is the current value of a one-year call option with an exercise price of $15? The six-month risk-free interest rate is 5% per six-month period.[Use the two-stage binomial method.]

A)$8.73
B)$10.03
C)$16.88
D)$13.33

Question 5

A call option has an exercise price of $100.At the exercise date,the stock price could be either $50 or $150.Which investment strategy provides the same payoff as the stock?

A)Lend PV of $50 and buy two calls.
B)Lend PV of $50 and sell two calls.
C)Borrow $50 and buy two calls.
D)Borrow $50 and sell two calls.

Question 6

A call option on ABCD stock,with an exercise price of $50,will either be worth $12 or worthless.The call option has a delta of 0.3.What is the binomial spread of possible stock prices?

A)low of $22 and high of $62
B)low of $50 and high of $62
C)low of $58 and high of $62
D)low of $38

Question 7

If the delta of a call option is 0.4,calculate the delta of an equivalent put option:

A)0.6.
B)0.4.
C)-0.4.
D)-0.6.

Question 8

Suppose ABC's stock price is currently $25.In the next six months it will either fall to $15 or rise to $40.What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5% (periodic rate).[Use the risk-neutral valuation method.]

A)$20.00
B)$8.57
C)$9.52
D)$13.10

Question 9

Suppose VS's stock price is currently $20.In the next six months it will either fall to $10 or rise to $30.What is the current value of a put option with an exercise price of $15? The six-month risk-free interest rate is 5% per six-month period.

A)$5.00
B)$2.14
C)$0.86
D)$7.86

Question 10

Why does a discounted cash-flow approach to options valuation not work?

A)It is impossible to estimate expected cash flows.
B)One cannot find the appropriate interest rate for an infinitely small interval.
C)Finding the opportunity cost of capital is impossible as the risk of options changes every time the stock price moves.
D)The strike price of options changes.

Question 11

Suppose ABCD's stock price is currently $50.In the next six months it will either fall to $40 or rise to $60.What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2% (periodic rate).

A)$5.39
B)$15.00
C)$8.25
D)$8.09

Question 12

Suppose ABCD's stock price is currently $50.In the next six months it will either fall to $40 or rise to $80.What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2% (periodic rate).

A)$2.40
B)$15.00
C)$8.25
D)$8.09

Question 13

Suppose VS's stock price is currently $20.In the next six months it will either fall by 50% or rise by 50%.What is the current value of a call option with an exercise price of $15 and expiration of one year? The six-month risk-free interest rate is 5% (periodic rate).Use the two stage binomial method.

A)$5.00
B)$2.14
C)$7.86
D)$8.23

Question 14

What is the current value of a six-month call option with an exercise price of $12? The six-month risk-free interest rate is 5% per six-month period.[Use the risk-neutral valuation method.]

A)$9.78
B)$10.28
C)$16.88
D)$13.33

Question 15

What is the current value of a six-month call option with an exercise price of $15? The six-month risk-free interest rate is 5% per six-month period.[Use the replicating portfolio method.]

A)$8.73
B)$10.28
C)$16.88
D)$13.33

Question 16

A put option on ABC stock currently sells for $4.00.The exercise price and the stock price is $60.The put option has a delta of 0.5.If within a short period of time the stock price increases to $60.10,what would be the change in the price of the put option?

A)increases by $0.05
B)decreases by $0.05
C)increases by $0.10
D)decreases by $0.10

Question 17

If the delta of a call option is 0.6,calculate the delta of an equivalent put option.

A)0.6
B)0.4
C)-0.4
D)-0.6

Question 18

The delta of a put option always equals:

A)the delta of an equivalent call option.
B)the delta of an equivalent call option with a negative sign.
C)the delta of an equivalent call option minus one.
D)the delta of an equivalent call option plus one.

Question 19

Suppose Ralph's stock price is currently $50.In the next six months it will either fall to $30 or rise to $80.What is the option delta of a call option with an exercise price of $50?

A)0.375
B)0.500
C)0.600
D)0.750

Question 20

Suppose VS's stock price is currently $20.A six-month call option on VS's stock with an exercise price of $15 has a value of $7.14.What is the price of an equivalent put option? The six-month risk-free interest rate is 5% per six-month period.

A)$1.43
B)$9.43
C)$8.00
D)$12.00

Question 21

If the standard deviation of the continuously compounded returns on the asset is 40% and the interval is a year,then the downside change is equal to:

A)-27.4%.
B)-53.6%.
C)-33.0%.
D)-38.7%.

Question 22

The Black-Scholes option pricing model employs which five parameters?

A)Stock price,exercise price,risk-free rate,beta,and time to maturity
B)Stock price,risk-free rate,beta,time to maturity,and variance
C)Stock price,risk-free rate,probability of bankruptcy,variance,and exercise price
D)Stock price,exercise price,risk-free rate,variance,and time to maturity

Question 23

The Black-Scholes formula represents the option delta as:

A)d₁
B)N(d₁)
C)d₂
D)N(d₂)

Question 24

Calculate d₂.

A)-0.02766
B)+0.02766
C)+0.2027
D)-0.2027

Question 25

If the value of d₂ is -0.5,then the value of N(d₂)is:

A)0.1915.
B)0.6915.
C)0.3085.
D)0.8085.

Question 26

If the standard deviation of the continuously compounded returns on the asset is 30% and the interval is a year,then the downside change is equal to:

A)-26%.
B)-54%.
C)-33%.
D)-39%.

Question 27

If the standard deviation of the continuously compounded returns on the asset is 20% and the interval is one half of a year,then the downside change is equal to:

A)-37.9%.
B)-19.3%.
C)-20.1%.
D)-13.2%.

Question 28

Calculate the value of d₁.

A)0.3
B)0.7
C)-0.7
D)0.5

Question 29

If the standard deviation of the continuously compounded returns (σ)on a stock is 40%,and the time interval is a year,then the upside change equals:

A)88.2%.
B)8.7%.
C)63.2%.
D)49.2%.

Question 30

A stock is currently selling for $50.The stock price could go up by 10% or fall by 5% each month.The monthly interest rate is 1% (periodic rate).Calculate the price of a call option on the stock with an exercise price of $50 and a maturity of two months.(Use the two-stage binomial method.)

A)$5.10
B)$2.71
C)$4.78
D)$3.62

Question 31

Important assumptions justifying the Black-Scholes formula include:
I.The price of the underlying asset follows a lognormal random walk.
II.Investors can adjust their hedge ratio continuously and at no cost.
III.The risk-free rate is known.
IV.The underlying asset does not pay dividends.

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

Question 32

All else equal,if an option's strike price increases then the:

A)value of a put option increases and that of a call option decrease.
B)value of a put option decreases and that of a call option increase.
C)value of both a put option and a call option increase.
D)value of both a put option and a call option decrease.

Question 33

If the value of d is -0.75,calculate the value of N(d):

A)0.2266.
B)0.6914.
C)0.7734.
D)0.5987.

Question 34

All else equal,if the volatility (variance)of the underlying stock increases,then the:

A)value of a put option increases and that of a call option decrease.
B)value of a put option decreases and that of a call option increase.
C)value of both a put option and a call option increase.
D)value of both a put option and a call option decrease.

Question 35

If u equals the quantity (1 + upside change),then the quantity (1 + downside change)is equal to:

A)-u.
B)-1/u.
C)1/u.
D)1 - u.

Question 36

Assume the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6% per year; Continuously compounded variance = 0.2; Expiration = three months.Calculate the value of a European call option.(Use the Black-Scholes formula.)

A)$7.62
B)$7.90
C)$5.00
D)$5.92

Question 37

If e is the base of natural logarithms,(σ)is the standard deviation of the continuously compounded annual returns on the asset,and h is the time to expiration,expressed as a fraction of a year,then the quantity (1 + upside change)is equal to:

A)e^[(σ)× SQRT(h)].
B)e^[h × SQRT(σ)].
C)(σ)× e^[SQRT(h)].
D)1/(σ)× e^[SQRT(h)].

Question 38

Calculate the value of d₂.

A)+0.0657
B)-0.0657
C)+0.5657
D)-0.5657

Question 39

If the value of d₁ is 1.25,then the value of N(d₁)is equal to:

A)0.1056.
B)1.2500.
C)0.2500.
D)0.8944.

Question 40

Calculate d₁.

A)0.0226
B)0.175
C)-0.3157
D)0.3157

Question 41

Which of the following statements about implied volatility is true?

A)VIX is the implied volatility on the Standard and Poor's index,and VXN is the implied volatility on the New York Stock Exchange Index.
B)VIX is the implied volatility on the Standard and Poor's index,and VXN is the implied volatility on the NASDAQ index.
C)VIX is the implied volatility on the NASDAQ index,and VXN is the implied volatility on the Standard and Poor's index.
D)VIX is the implied volatility on the New York Stock Exchange index,and VXN is the implied volatility on the Standard and Poor's index.

Question 42

Why does the Black-Scholes call formula use the present value of the exercise price and not merely the exercise price in the formula?

A)All finance must use the time value of money.
B)Call options are rarely exercised early.
C)The present value accounts for a potential dividend.
D)The put option

Question 43

The value of a call option increases as the risk-free interest rate increases.

Question 44

For lookback options:

A)the option holder must decide before maturity whether the option is a call or a put.
B)the option holder chooses as the exercise price any of the asset prices that occurred before the final date.
C)the option payoff is zero if the asset price is on the wrong side of the exercise price and otherwise is a fixed sum.
D)the exercise price is equal to the average of the asset's price during the life of the option.

Question 45

The delta of a put option equals the delta of an equivalent call option minus one.

Question 46

N(d₁)in the Black-Scholes model represents:
I.the call option delta;
II.a hedge ratio;
III.the cumulative probability function

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

Question 47

For a European option: Value of put = (value of call)- share price + PV (exercise price).

Question 48

The binomial option pricing model is a discrete time model.

Question 49

Suppose the exchange rate between the U.S.dollar and the British pound is US$1.50 = BP1.00.If the interest rate is 6% per year,what is the adjusted price of the British pound when valuing a foreign currency option with an expiration of one year?

A)$1.9050
B)$1.4151
C)$0.7067
D)$1.5900

Question 50

The option delta for a put option is always positive.

Question 51

Considering the standard deviation of returns in option pricing: 1 + upside change = u = e^(σ)(√h).

Question 52

Which of the following statements regarding American puts is/are true?

A)An American put can be exercised any time before expiration.
B)An American put is always more valuable than an equivalent European put.
C)A multi-period binomial model can be used to value an American put.
D)All of the options

Question 53

It is possible to replicate an investment in a call option by a levered investment in the underlying asset.

Question 54

The Black-Scholes model is a discrete time model.

Question 55

For Asian options:

A)the option is exercisable on discrete dates before maturity.
B)the option holder chooses as the exercise price any of the asset prices that occurred before the final date.
C)the option payoff is zero if the asset price is on the wrong side of the exercise price and otherwise is a fixed sum.
D)the exercise price is equal to the average of the asset's price during the life of the option.

Question 56

As you increase the time per interval in a binomial model,the result will approach the Black-Scholes model.

Question 57

The term [N(d₂)× PV(EX)] in the Black-Scholes model represents the:

A)call option delta.
B)bank loan.
C)put option delta.
D)present value of a bank loan.

Question 58

A stock is currently selling for $50.The stock price could go up by 10% or fall by 5% each month.The monthly risk-free interest rate is 1%.Calculate the price of an American put option on the stock with an exercise price of $55 and a maturity of two months.(Use the two-stage binomial method.)

A)$5.10
B)$3.96
C)$4.78
D)$1.19

Question 59

The value of N(d),which is used in the Black-Scholes model,can take any value between:

A)-1 and +1.
B)0 and +1.
C)-1 and 0.
D)-0.95 and 0.95.

Question 60

N(d₁)and N(d₂)represent cumulative probabilities and therefore take values between 0 and 1.

Question 61

Explain what implied volatility,as measured by the VIX,may mean to the overall stock market.

Question 62

A knock-in barrier option might be used if the investor is looking to reduce the cost of buying a call option.

Question 63

Briefly explain how to choose the up and down values for the binomial method.

Question 64

Briefly explain why the discounted cash-flow method (DCF)does not work for valuing options.

Question 65

An option holder is not entitled to any dividends paid on the underlying stock.

Question 66

One should use a multiperiod binomial model to evaluate an American put option because the Black-Scholes formula does not allow for early exercise.

Question 67

The smaller the time periods used in the binomial model the closer it will come to approximating the Black-Scholes' model price.

Question 68

Briefly explain what is meant by risk-neutral probability.

Question 69

Briefly explain why a call option is always riskier than a simple investment in the underlying stock.

Question 70

Briefly discuss risk-neutral valuation in the context of option valuation.

Question 71

Briefly explain put-call parity.

Question 72

Give an example of an option equivalent investment using common stock and borrowing.

Question 73

Suppose an investor wishes to "cash-in" an in-the-money American call option (on a nondividend paying stock)that has lots of time until expiration.The investor will be better off trading the option to another investor rather than exercising the option early.

Question 74

To find the beta of a call option,one can calculate the portfolio beta of the replicating stock and risk-free loan.

Question 75

Briefly explain the term option delta.