Chapter Six



Chapter Six

The Black-Scholes Option Pricing Model

Multiple Choice

1. In the Black-Scholes Option Pricing Model, what is the minimum and maximum value of N(d1)?

a. minus infinity to plus infinity

b. minus infinity to zero

c. minus one to zero

d. zero to plus infinity

ANSWER: A

2. In the Black-Scholes Option Pricing Model, if interest rates rise, the price of a call option will

a. decline.

b. remain unchanged.

c. increase.

d. decline, then increase.

ANSWER: C

3. All of the following are assumptions of the Black-Scholes Option Pricing Model except

a. markets are efficient.

b. no dividends.

c. interest rates are constant.

d. investors are generally bullish.

ANSWER: D

4. The expected volatility of the underlying asset is known as

a. sigma.

b. delta.

c. gamma.

d. theta.

ANSWER: A

5. Option value is mostly concerned with

a. historical volatility

b. average daily volatility.

c. expected future volatility.

d. market average volatility.

ANSWER: C

6. If volatility increases, call premiums _____ and put premiums _____.

a. increase, increase

b. increase, decrease

c. decrease, increase

d. decrease, decrease

ANSWER: A

7. A method of adjusting for cash dividends is the _____ model.

a. Fisher

b. Sharpe

c. Merton

d. Miller

ANSWER: C

8. Everything else being equal, an American option will sell for ________ a European option.

a. more than

b. less than

c. the same as

d. None of the above; cannot be determined

ANSWER: A

9. The Black-Scholes model assumes a _____ distribution.

a. lognormal

b. uniform

c. triangular

d. Poisson

ANSWER: A

10. Which of the following is most accurate?

a. Implied volatility is usually less than historical volatility.

b. Implied volatility is usually greater than historical volatility.

c. Implied volatility is usually equal to historical volatility.

d. There is no reliable connection between historical and implied volatility.

ANSWER: D

11. Option traders often price options in _____ units.

a. delta

b. volatility

c. theta

d. Eurodollar

ANSWER: B

12. The plot of implied volatility values as a function of the stock price is known as a

a. yield curve.

b. volatility smile.

c. volatility decay plot.

d. volatility diffusion diagram.

ANSWER: B

13. The option to defer something is an example of a(n) _____ option.

a. exotic

b. lookback

c. real

d. barrier

ANSWER: C

14. The Black-Scholes model works best with options that are

a. deep out-of-the-money.

b. out-of-the-money

c. at-the-money

d. in-the-money.

ANSWER: C

Short Answer/Problem

1. A non-dividend paying stock sells for $23 3/8. What is the theoretical value of a European style, $25 call with 50 days until expiration, assuming interest rates of 6% and annual volatility of 25%?

ANSWER: Using the CBOE options calculator, the theoretical value is $0.35.

2. Estimate the value of the option in Problem 1 if it were American style instead of European.

ANSWER: An American option should sell for more than a European option. The CBOE calculator indicates a theoretical value of $0.36.

3. You are going to use the Black-Scholes option pricing model on a six-month call option that has the following expected dividend stream; short term interest rates are 5%.

|Time until dividend |2 months |5 months |8 months |

|Expected dividend |$1.00 |$1.00 |$1.05 |

If the current stock price is $105, what is the adjusted stock price you would use as a BSOPM input?

ANSWER:

Only dividends over the option’s life matter. S’ = S – PV (dividends)

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