[OFOD10e15] The Black-Scholes-Merton Model

1.Which of the following is assumed by the Black-Scholes-Merton model?

A.The return from the stock in a short period of time is lognormal

B.The stock price at a future time is lognormal

C.The stock price at a future time is normal

D.None of the above

2.The original Black-Scholes and Merton papers on stock option pricing were published in which year?

A.1983

B.1984

C.1974

D.1973

3.Which of the following is a definition of volatility

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

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

A.$0.38

B.$2.77

C.$3.02

D.$0.76

5.What does N(x) denote?

A.The area under a normal distribution from zero to x

B.The area under a normal distribution up to x

C.The area under a normal distribution beyond x

D.The area under the normal distribution between -x and x

6.Which of the following is true for a one-year call option on a stock that pays dividends every three months?

A.It is never optimal to exercise the option early

B.It can be optimal to exercise the option at any time

C.It is only ever optimal to exercise the option immediately after an ex-dividend date

D.None of the above

7.What is the number of trading days in a year usually assumed for equities?

A.365

B.252

C.262

D.272

8.The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%. Which of the following is a way of valuing a derivative?

A.Assume that the expected growth rate for the stock price is 17% and discount 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 12% and discounting the expected payoff at 5%

9.When there are two dividends on a stock, Black’s approximation sets the value of an American call option equal to which of the following

A.The value of a European option maturing just before the first dividend

B.The value of a European option maturing just before the second (final) dividend

C.The greater of the values in A and B

D.The greater of the value in B and the value assuming no early exercise

10.Which of the following is measured by the VIX index

A.Implied volatilities for stock options trading on the CBOE

B.Historical volatilities for stock options trading on 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

11.What was the original Black-Scholes-Merton model designed to value?

A.A European option on a stock providing no dividends

B.A European or American option on a stock providing no dividends

C.A European option on any stock

D.A European or American option on any stock

12.A stock provides an expected return of 10% per year and has a volatility of 20% per year. What is the expected value of the continuously compounded return in one year?

A.6%

B.8%

C.10%

D.12%

13.An investor has earned 2%, 12% and -10% on equity investments in successive years (annually compounded). This is equivalent to earning which of the following annually compounded rates for the three year period.

A.1.33%

B.1.23%

C.1.13%

D.0.93%

14.Which of the following is NOT true?

A.Risk-neutral valuation provides prices that are only correct in a world where investors are risk-neutral

B.Options can be valued based on the assumption that investors are risk neutral

C.In risk-neutral valuation the expected return on all investment assets is set equal to the risk-free rate

D.In risk-neutral valuation the risk-free rate is used to discount expected cash flows

15.Which of the following is a way of extending the Black-Scholes-Merton formula to value a European call option on a stock paying a single dividend?

A.Reduce the maturity of the option so that it equals the time of the dividend

B.Subtract the dividend from the stock price

C.Add the dividend to the stock price

D.Subtract the present value of the dividend from the stock price

16.When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true?

A.The binomial tree price converges to a price slightly above the Black-Scholes-Merton price as the number of time steps is increased

B.The binomial tree price converges to a price slightly below the Black-Scholes-Merton price as the number of time steps is increased

C.Either A or B can be true

D.The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased

17.When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock

A.20N(0.1)-19.7N(0.2)

B.20N(0.2)-19.7N(0.1)

C.19.7N(0.2)-20N(0.1)

D.19.7N(0.1)-20N(0.2)

18.When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock

A.19.7N(-0.1)-20N(-0.2)

B.20N(-0.1)-20N(-0.2)

C.19.7N(-0.2)-20N(-0.1)

D. 20N(-0.2)-20N(-0.1)

19.A stock price is 20, 22, 19, 21, 24, and 24 on six successive Fridays. Which of the following is closest to the volatility per annum estimated from this data?

A.50%

B.60%

C.70%

D.80%

20.The volatility of a stock is 18% per year. Which is closest to the volatility per month?

A.1.5%

B.3.0%

C.5.2%

D.6.3%

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