Question 1

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 2

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 B

Question 3

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% C

Question 4

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 5

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 6

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?

Accepted Answer

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

Question 7

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 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

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 10

Which of the following is NOT true?

Accepted Answer

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 
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

Question 11

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

Accepted Answer

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 
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

Question 12

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 13

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

Question 14

When the non-dividend paying stock price is $20,the strike price is $20,the risk-free rate is 5%,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 15

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 16

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

Question 17

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

Accepted Answer

A) 1.5% 
B) 3.0% 
C) 5.2% 
D) 6.3% 
A) 1.5% 
B) 3.0% 
C) 5.2% 
D) 6.3%

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

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 20

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

Exam 15: The Black-Scholes-Merton Model

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?

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

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?

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

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 expected value of the continuously compounded return in one year?

Which of the following is a definition of volatility

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?

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 NOT true?

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

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

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?

When the non-dividend paying stock price is $20,the strike price is $20,the risk-free rate is 5%,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 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 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?

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

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

What does N(x)denote?

Which of the following is measured by the VIX index

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

OIS Discounting, Credit Issues, and Funding Costs

Mechanics of Options Markets

Properties of Stock Options

Trading Strategies Involving Options

Binomial Trees

Wiener Processes and Ito’s Lemma

Employee Stock Options

Options on Stock Indices and Currencies

Futures Options

The Greek Letters

Volatility Smiles

Basic Numerical Procedures

Value at Risk

Estimating Volatilities and Correlations

Credit Risk

Credit Derivatives

Exotic Options

Filters