21: Option Valuation

Question 1

Intrinsic Value Definition

Answer 1

The present value of a firm’s expected future net cash flows discounted by the required rate of return.

Question 2

Time Value Definition

Answer 2

The part of the value of an option that is due to positive time to expiration.

Question 3

Binomial Model Definition

Answer 3

An option valuation model predicted using the assumption that the stock price can move to only two values over a short time period.

Question 4

Black-Scholes Pricing Formula

Answer 4

An equation to value a call option.

Question 5

Implied Volatility Definition

Answer 5

The standard deviation of stock returns that is consistent with an option’s market value.

Question 6

Pseudo-American Call Option Value Definition

Answer 6

The maximum of the value derived by the assumptions that the option will be held until expiration and the option will be exercised just before an ex-dividend date.

Question 7

Hedge Ratio (Delta) Definition

Answer 7

The number of stocks required to hedge against the price risk of holding one option.

Question 8

Option Elasticity Definition

Answer 8

The % increase in an option’s value given a 1% change in the value of the underlying asset.

Question 9

Portfolio Insurance Definition

Answer 9

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

Question 10

Dynamic (Delta) Hedging Definition

Answer 10

Constant updating of hedge positions as market conditions change.

Question 11

Gamma Definition

Answer 11

The curvature of an option-pricing function as a function of the value of the underlying asset.

Question 12

Delta-Neutral Definition

Answer 12

The value of the portfolio is not affected by changes in the underlying asset.

Question 13

Vega Definition

Answer 13

Response of option prices to changes in the standard deviation of the underlying asset.

Question 14

How are options valued?

Answer 14

As the sum of their time value plus their intrinsic value.

Question 15

What is the maximum an option holder can lose?

Answer 15

100% of the initial investment.

Question 16

Lower exercise prices result in _______ call option prices.

Answer 16

Higher

Question 17

Lower dividend payments result in _______ call option prices.

Answer 17

Higher

Question 18

Lower stock prices result in _______ call option prices.

Answer 18

Lower

Question 19

Lower interest rates result in _______ call option prices.

Answer 19

Lower

Question 20

Lower volatility result in _______ call option prices.

Answer 20

Lower

Question 21

Less time to expiration results in _______ call option prices.

Answer 21

Lower

Question 22

Greater exercise prices result in _________ call option prices.

Answer 22

Lower

Question 23

Greater stock prices result in _________ call option prices.

Answer 23

Higher

Question 24

Greater interest rates result in _________ call option prices.

Answer 24

Higher

Question 25

Greater time to expiration results in _________ call option prices.

Answer 25

Higher

Question 26

Greater volatility results in _________ call option prices.

Answer 26

Higher

Question 27

Greater dividend payments result in _________ call option prices.

Answer 27

Lower

Question 28

What is the minimum price of a call option?

Answer 28

S - PV(X) - PV(d) The stock price minus the present value of the exercise price and the present value of any dividends to be paid before expiration.

Question 29

When is there incentive to exercise a call option early?

Answer 29

When the call option pays dividends before the expiration date?

Question 30

Is there any benefit to exercising a call option on a non-dividend paying stock early?

Answer 30

No.

Question 31

As n -> infinity, does the binomial model get more or less accurate?

Answer 31

More accurate

Question 32

Is the Black-Scholes formula more or less limiting than the binomial model?

Answer 32

More limiting

Question 33

When can the Black-Scholes formula be easily adjusted for dividend payments?

Answer 33

When it is pricing European call options. It cannot be easily adjusted for American call options on stocks that pay dividends.

Question 34

Are American or European put options worth more, all else held equal?

Answer 34

American put options because there can be value to exercising early.

Question 35

Can American put prices be derived from the put-call parity relationship?

Answer 35

No because they can be exercised early.

Question 36

How can implied volatility be calculated?

Answer 36

Using the option-pricing model to find the stock volatility that makes an option's value equal to its observed price.

Question 37

When are hedge ratios near 0?

Answer 37

For deeply out-of-the-money call options.

Question 38

When are hedge ratios near 1?

Answer 38

For deeply in-the-money call options.

Question 39

Can hedge ratios for call options be greater than 1?

Answer 39

No

Question 40

Can elasticities of call options be greater than 1?

Answer 40

Yes. The rate of return on a call responds more than one-for-one with stock price movement.

Question 41

How can portfolio insurance be obtained for an equity position?

Answer 41

By buying a protective put option on that equity position, or using a dynamic hedging strategy.

Question 42

Are delta-neutral portfolios independent of price changes in the underlying asset?

Answer 42

Yes

Question 43

Are delta-neutral portfolios independent of volatility changes in the underlying asset?

Answer 43

Yes