Question 1

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?

Accepted Answer

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 
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 D

Question 2

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?

Accepted Answer

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

Question 3

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?

Accepted Answer

A) 50% 
B) 60% 
C) 70% 
D) 80% 
A) 50% 
B) 60% 
C) 70% 
D) 80% D

Question 4

Which of the following is a definition of volatility?

Accepted Answer

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 
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

Question 5

Which of the following is NOT true?

Accepted Answer

A) Risk-neutral valuation assumes that 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 
A) Risk-neutral valuation assumes that 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

Question 6

The volatility of a stock is 18% per year.What is the volatility per month?

Accepted Answer

A) 1.5% 
B) 3.0% 
C) 5.2% 
D) None of the above 
A) 1.5% 
B) 3.0% 
C) 5.2% 
D) None of the above

Question 7

Which of the following is measured by the VIX index?

Accepted Answer

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 
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

Question 8

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?

Accepted Answer

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 
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

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

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 
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

Question 11

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?

Accepted Answer

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% 
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%

Question 12

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

Accepted Answer

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 
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

Question 13

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

Accepted Answer

A) 6% 
B) 8% 
C) 10% 
D) 12% 
A) 6% 
B) 8% 
C) 10% 
D) 12%

Question 14

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

Accepted Answer

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 
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

Question 15

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

Accepted Answer

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

Question 16

What does N(x)denote?

Accepted Answer

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 
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

Question 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 put option on the stock?

Accepted Answer

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) 
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)

Question 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 call option on the stock?

Accepted Answer

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) 
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)

Question 19

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.

Accepted Answer

A) 1.33% 
B) 1.23% 
C) 1.13% 
D) 0.93% 
A) 1.33% 
B) 1.23% 
C) 1.13% 
D) 0.93%

Question 20

Which of the following is true when there are dividends?

Accepted Answer

A) It is never optimal to exercise a call option on the stock 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 
A) It is never optimal to exercise a call option on the stock 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

Exam 13: Valuing Stock Options: The BSM Model

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 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 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?

Which of the following is a definition of volatility?

Which of the following is NOT true?

The volatility of a stock is 18% per year.What is the volatility per month?

Which of the following is measured by the VIX index?

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?

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

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?

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?

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

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

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

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

What does N(x)denote?

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?

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?

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.

Which of the following is true when there are dividends?

Introduction

Mechanics of Futures Markets

Hedging Strategies Using Futures

Interest Rates

Determination of Forward and Futures Prices

Interest Rate Futures

Swaps

Securitization and the Credit Crisis of 2007

Mechanics of Options Markets

Properties of Stock Options

Trading Strategies Involving Options

Introduction to Binomial Trees

Employee Stock Options

Options on Stock Indices and Currencies

Futures Options

The Greek Letters

Binomial Trees in Practice

Volatility Smiles

Value at Risk

Interest Rate Options

Exotic Options and Other Nonstandard Products

Credit Derivatives

Weather, Energy, and Insurance Derivatives

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