Deck 21: Valuing Options

Question 1

A call option on the ABCD stock, with an exercise price of $50, is selling for $5.00 and the stock price is also $50. The call option has a delta of 0.3. If within a short period of time the stock price increases to $52, what would be the change in the price of the call option?

A) increases by $0.60
B) decreases by $0.60
C) increases by $2.00
D) decreases by $2.00

Answer 1

increases by $0.60

Question 2

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

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

Answer 2

$9.78

Question 3

The delta of a put option is always equal to:

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) None of the above

Answer 3

The delta of an equivalent call option minus one

Question 4

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% (periodic rate). [Use the replicating portfolio method]

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

Question 5

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 6

Suppose VS's stock price is currently $20. Six-month call option on the stock with an exercise price of $15 has a value of $7.14. Calculate the price of an equivalent put option if the six-month risk-free interest rate is 5% (periodic rate).

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

Question 7

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

Question 8

A put option on the ABC stock, with an exercise price of $60, is selling for $4.00 and the stock price is also $60. The put option has a delta of 0.5. If within a short period of time the stock price increases to $61, what would be the change in the price of the put option?

A) increases by $0.50
B) decreases by $0.50
C) increases by $1.00
D) decreases by $1.00

Question 9

A call option has an exercise price of $100. At the final exercise date, the stock price could be either $50 or $150. Which investment would combine to give 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 10

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 11

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 12

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 13

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

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

Question 14

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) 0.75

Question 15

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 put 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 16

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% (periodic rate).

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

Question 17

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 18

Discounted cash flow approach to valuation does not work in the case of options because:

A) it is possible to but difficult to estimate the expected cash flows.
B) the estimated cash flows have to be discounted at the opportunity cost of capital.
C) finding the opportunity cost of capital is impossible as the risk of options change every time the stock price moves.
D) (B) and (C) above

Question 19

An equity option's theoretical delta reflects the sensitivity of its market price to changes in:

A) the volatility of the underlying stock price
B) the dividends paid to the underlying stockholders
C) the underlying stock price
D) the time to expiration

Question 20

Suppose Caroll's stock price is currently $20. In the each next six month periods 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 (periodic rate) is 5%. [Use the two stage binomial method]

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

Question 21

Calculate the value of d2 (approximately).

A) +0.0656
B) -0.0656
C) +0.5656
D) -0.5656

Question 22

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

A) 0.2266
B) -0.2266
C) 0.7734
D) -0.2734

Question 23

If the strike price increases then the: [Assume everything else remaining the same]

A) Value of the put option increases and that of the call option decreases
B) Value of the put option decreases and that of the call option increases
C) Value of both the put option and the call option increases
D) Value of both the put option and the call option decreases

Question 24

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 25

Given the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6%; variance = 0.2 ; Expiration = 3 months. Calculate value of a European call option: [Use Black-Scholes Formula]

A) $7.62
B) $7.90
C) $5.00
D) none of the above

Question 26

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) none of the above.

Question 27

If the volatility (variance) of the underlying stock increases then the: [Assume everything else remaining the same]

A) Value of the put option increases and that of the call option decreases
B) Value of the put option decreases and that of the call option increases
C) Value of both the put option and the call option increases
D) Value of both the put option and the call option decreases

Question 28

The Black-Scholes OPM is dependent on 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, variance and exercise price
D) Stock price, exercise price, risk free rate, variance and time to maturity

Question 29

Calculate the value of d2: (approximately)

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

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 European 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

The important assumptions of the Black-Scholes formula are:
I. the price of the underlying asset follows a lognormal random walk. II) investors can adjust their hedge 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

If the standard deviation of the annual returns (σ ) on the asset is 40%, and the time interval is a year, then the upside change is equal to:

A) 88.2%
B) 8.7%
C) 63.2%
D) 49.18%

Question 33

If the standard deviation for annual 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) 32.97%
D) 38.7%

Question 34

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

A) -0.1056
B) 1.25
C) 0.25
D) 0.8944

Question 35

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

A) 26%
B) 53.6%
C) 33.0%
D) 38.7%

Question 36

Then [d1] has a value of (approximately):

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

Question 37

The option delta in the case of Black-Scholes formula is:

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

Question 38

The value of [d1] is (approximately):

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

Question 39

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

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

Question 40

If e is the base of natural logarithms, and (σ) is the standard deviation of the continuously compounded annual returns on the asset, and h is the interval 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) none of the above.

Question 41

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

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

Question 42

1 + upside change = u = e^(σ)(Öh).

Question 43

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

Question 44

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

A) call option delta
B) bank loan
C) put option delta
D) none of the above

Question 45

The binomial model is a discrete time model.

Question 46

Delta of a put option is equal to the delta of an equivalent call option minus one.

Question 47

Option delta for a put option is always positive.

Question 48

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 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) None of the above

Question 49

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 50

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) You cannot exercise an option early
D) Because the put option uses the future value

Question 51

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) Multi-period binomial model can be used to value an American put
D) All of the above

Question 52

In the case of Asian option:

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 53

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

A) -1 and +1
B) 0 and +1
C) -1 and 0
D) None of the above

Question 54

Using the binomial model, what is the value of a three month option given the following data and assuming there are no time periods other than three months? The exercise price is
$40; stock price is $46; the upside price is $48; the downside price is $34; the 3 month interest rate is 2%. The upside and down side have equal probabilities.

A) $3.92
B) $4.00
C) $5.88
D) $6.00

Question 55

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

Question 56

In the case of look back option:

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 57

The Black-Scholes model is a discrete time model.

Question 58

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

Question 59

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

Question 60

Suppose the exchange rate between US dollars and 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? (Approximately)

A) $1.905
B) $1.4151
C) $0.7067
D) None of the above

Question 61

Briefly explain why an option is always riskier than the underlying stock.

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

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

Question 64

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

Question 65

Multi-period binomial model can be used to evaluate an American put option.

Question 66

Briefly explain what is meant by risk-neutral probability.

Question 67

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

Question 68

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

Question 69

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

Question 70

Briefly explain put-call parity.

Question 71

Briefly explain the term "option delta."

Question 72

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