Deck 13: Valuing Stock Options: the Black-Scholes-Merton Model

Question 1

When there are dividends: choose one)

A) It is never optimal to exercise a call option early
B) It can be optimal to exercise a call option at any time
C) It is only ever optimal to exercise a call option immediately after an ex-dividend date
D) None of the above

Answer 1

D

Question 2

For equities it is usually assumed that the number of trading days in the year is:

A) 365
B) 252
C) 262
D) 272

Answer 2

B

Question 3

The risk-free rate is 5% and the expected return on a stock is 12%. A derivative can be valued by: choose one)

A) Assuming that the expected growth rate for the stock price is 13% and discounting the expected payoff at 12%
B) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 12%
C) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5%
D) Assuming that the expected growth rate for the stock price is 13% and discounting the expected payoff at 5%

Answer 3

C

Question 4

A 7-month European put option on the stock of Telstra has an exercise price of $4.80. The current stock price is $4.50, the risk-free rate is 8% per annum, and the volatility is 30% per annum. Calculate the price of the put option using the Black-Scholes-Merton formula. _ _ _ _ _ _ _ _

Question 5

In the Black-Scholes-Merton option pricing formula, Nd₁) denotes: choose one)

A) The area under a normal distribution from zero to d₁
B) The area under a normal distribution up to d₁
C) The area under a normal distribution beyond d₁
D) The area under a normal distribution between -d₁ and d₁

Question 6

A stock price is $100. Volatility is estimated to be 20% per year. What is the estimate of the standard deviation of the change in the stock price in one week? choose one)

A) $0.38
B) $2.77
C) $3.02
D) $0.76

Question 7

The Black-Scholes-Merton model assumes: choose one)

A) The return from the stock in a short period of time is lognormally distributed
B) The stock price at a future time is lognormally distributed
C) The stock price at a future time is normally distributed
D) None of the above

Question 8

The VIX index measures choose one)

A) Implied volatilities for stock options trading on the CBOE
B) Historical volatilities for stock options trading on the CBOE
C) Implied volatilities for options trading on the S&P 500 Index
D) Historical volatilities for options trading on the S&P 500 Index

Question 9

What is the price of the put option in the previous question if there is a dividend payment of $0.40 in 3 months? _ _ _ _ _ _ _ _

Question 10

The Black, Scholes and Merton pathbreaking papers on stock option pricing were published in: choose one)

A) 1983
B) 1984
C) 1974
D) 1973

Question 11

Volatility can be defined as: choose one)

A) The standard deviation of the return, measured with continuous compounding, in one year
B) The variance of the return, measured with continuous compounding, in one year
C) The standard deviation of the stock price in one year
D) The variance of the stock price in one year