Question 1

Which of the following is true of maximum likelihood methods

Accepted Answer

A)  They calculate the maximum possible values for parameters 
B)  They calculate parameters that give the highest probability of past data occurring 
C)  They calculate values for key variables that are most likely to occur in the future 
D)  They involve a multivariate regression analysis 
A)  They calculate the maximum possible values for parameters 
B)  They calculate parameters that give the highest probability of past data occurring 
C)  They calculate values for key variables that are most likely to occur in the future 
D)  They involve a multivariate regression analysis B

Question 2

Which of the following is true

Accepted Answer

A)  GARCH models incorporate mean reversion; EWMA models do not 
B)  EWMA models incorporate mean reversion; GARCH models do not 
C)  Both GARCH and EWMA models incorporate mean reversion 
D)  Neither GARCH nor EWMA models incorporate mean reversion 
A)  GARCH models incorporate mean reversion; EWMA models do not 
B)  EWMA models incorporate mean reversion; GARCH models do not 
C)  Both GARCH and EWMA models incorporate mean reversion 
D)  Neither GARCH nor EWMA models incorporate mean reversion A

Question 3

Which of the following is true when the parameter lambda equals 0.95?

Accepted Answer

A)  The weight given to the most recent observation is 0.95 
B)  The weight given to the observation one day ago is 95% of the weight given to the observation two days ago 
C)  The weights given to observations add up to 0.95 
D)  The weights given to the observation two days ago is 95% of the weight given to the observation one day ago 
A)  The weight given to the most recent observation is 0.95 
B)  The weight given to the observation one day ago is 95% of the weight given to the observation two days ago 
C)  The weights given to observations add up to 0.95 
D)  The weights given to the observation two days ago is 95% of the weight given to the observation one day ago D

Question 4

Which of the following is true

Accepted Answer

A)  GARCH (1,1) will always give a maximum likelihood at least as high as EWMA 
B)  EWMA will always give a maximum likelihood at least as high as GARCH (1,1) 
C)  The maximum likelihood is the same for GARCH (1,1) and EWMA 
D)  Sometimes A is true and sometimes B is true. 
A)  GARCH (1,1) will always give a maximum likelihood at least as high as EWMA 
B)  EWMA will always give a maximum likelihood at least as high as GARCH (1,1) 
C)  The maximum likelihood is the same for GARCH (1,1) and EWMA 
D)  Sometimes A is true and sometimes B is true.

Question 5

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.Which of the following is the closest to the long run average volatility?

Accepted Answer

A)  1.1% 
B)  1.2% 
C)  1.3% 
D)  1.4% 
A)  1.1% 
B)  1.2% 
C)  1.3% 
D)  1.4%

Question 6

At the end of Thursday,the estimated volatility of asset B is 1% per day.During Friday asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset B at the end of Friday?

Accepted Answer

A)  0.98% 
B)  0.95% 
C)  0.92% 
D)  0.90% 
A)  0.98% 
B)  0.95% 
C)  0.92% 
D)  0.90%

Question 7

Which of the following is true

Accepted Answer

A)  EWMA is a particular case of GARCH (1,1) where the reversion rate is zero 
B)  EWMA has a lower reversion rate than GARCH (1,1), but it is not zero 
C)  EWMA has a higher reversion rate than GARCH (1,1) 
D)  Sometimes EWMA has a higher reversion rate than GARCH (1,1) and sometimes it has a lower reversion rate than GARCH (1,1). 
A)  EWMA is a particular case of GARCH (1,1) where the reversion rate is zero 
B)  EWMA has a lower reversion rate than GARCH (1,1), but it is not zero 
C)  EWMA has a higher reversion rate than GARCH (1,1) 
D)  Sometimes EWMA has a higher reversion rate than GARCH (1,1) and sometimes it has a lower reversion rate than GARCH (1,1).

Question 8

Which of the following is a definition of the covariance between X and Y?

Accepted Answer

A)  Correlation between X and Y times variance of X times variance of Y 
B)  Variance of X times the variance of Y 
C)  Correlation between X and Y divided by the product of the standard deviation of X and the standard deviation of Y 
D)  Correlation between X and Y times standard deviation of X times standard deviation of Y 
A)  Correlation between X and Y times variance of X times variance of Y 
B)  Variance of X times the variance of Y 
C)  Correlation between X and Y divided by the product of the standard deviation of X and the standard deviation of Y 
D)  Correlation between X and Y times standard deviation of X times standard deviation of Y

Question 9

Which of the following is true of a positive semi-definite variance-covariance matrix

Accepted Answer

A)  All elements of the matrix are positive 
B)  The determinant of the matrix is positive 
C)  The matrix has ones on the diagonal 
D)  The matrix is internally consistent 
A)  All elements of the matrix are positive 
B)  The determinant of the matrix is positive 
C)  The matrix has ones on the diagonal 
D)  The matrix is internally consistent

Question 10

At the end of Thursday,the estimated covariance between assets A and B is 0.0001.During Friday asset A produces a return of 3% and asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the covariance at the end of Friday?

Accepted Answer

A)  0.000090 
B)  0.000081 
C)  0.000100 
D)  0.000095 
A)  0.000090 
B)  0.000081 
C)  0.000100 
D)  0.000095

Question 11

If the volatility for a portfolio is 20% per year,what is the volatility per quarter?

Accepted Answer

A)  20% 
B)  10% 
C)  5% 
D)  2% 
A)  20% 
B)  10% 
C)  5% 
D)  2%

Question 12

At the end of Thursday,the estimated volatility of asset A is 2% per day.During Friday asset A produces a return of 3%.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset A at the end of Friday?

Accepted Answer

A)  2.08% 
B)  2.10% 
C)  2.12% 
D)  2.14% 
A)  2.08% 
B)  2.10% 
C)  2.12% 
D)  2.14%

Question 13

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.If we observe a change in the value of the variable equal to 2%,how does the estimate of the volatility change

Accepted Answer

A)  1.26% 
B)  1.16% 
C)  1.06% 
D)  1.03% 
A)  1.26% 
B)  1.16% 
C)  1.06% 
D)  1.03%

Question 14

Which of the following is true

Accepted Answer

A)  All option implied volatilities tend to move by the same amount from one day to the next 
B)  The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options 
C)  The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options 
D)  Sometimes B is true and sometimes C is true 
A)  All option implied volatilities tend to move by the same amount from one day to the next 
B)  The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options 
C)  The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options 
D)  Sometimes B is true and sometimes C is true

Question 15

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.What is the reversion rate for the variance rate implied by the model

Accepted Answer

A)  0.5% per day 
B)  1.0% per day 
C)  1.5% per day 
D)  2.0% per day 
A)  0.5% per day 
B)  1.0% per day 
C)  1.5% per day 
D)  2.0% per day

Question 16

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.What is the expected volatility in 20 days?

Accepted Answer

A)  1.09% 
B)  1.10% 
C)  1.11% 
D)  1.12% 
A)  1.09% 
B)  1.10% 
C)  1.11% 
D)  1.12%

Question 17

What does EWMA stand for?

Accepted Answer

A)  Equally weighted moving average 
B)  Equally weighted median approximation 
C)  Exponentially weighted moving average 
D)  Exponentially weighted median average 
A)  Equally weighted moving average 
B)  Equally weighted median approximation 
C)  Exponentially weighted moving average 
D)  Exponentially weighted median average

Question 18

Which of the following is true

Accepted Answer

A)  Volatilities and correlations decreased in the second half of 2008 
B)  Volatilities and correlations increased in the second half of 2008 
C)  Volatilities decreased and correlations increased in the second half of 2008 
D)  Volatilities increased and correlations decreased in the second half of 2008 
A)  Volatilities and correlations decreased in the second half of 2008 
B)  Volatilities and correlations increased in the second half of 2008 
C)  Volatilities decreased and correlations increased in the second half of 2008 
D)  Volatilities increased and correlations decreased in the second half of 2008

Question 19

How many parameters are necessary to define a GARCH (1,1)model

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Question 20

How many parameters are necessary to define an EWMA model

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Exam 23: Estimating Volatilities and Correlations

Which of the following is true of maximum likelihood methods

Which of the following is true

Which of the following is true when the parameter lambda equals 0.95?

Which of the following is true

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.Which of the following is the closest to the long run average volatility?

At the end of Thursday,the estimated volatility of asset B is 1% per day.During Friday asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset B at the end of Friday?

Which of the following is true

Which of the following is a definition of the covariance between X and Y?

Which of the following is true of a positive semi-definite variance-covariance matrix

At the end of Thursday,the estimated covariance between assets A and B is 0.0001.During Friday asset A produces a return of 3% and asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the covariance at the end of Friday?

If the volatility for a portfolio is 20% per year,what is the volatility per quarter?

At the end of Thursday,the estimated volatility of asset A is 2% per day.During Friday asset A produces a return of 3%.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset A at the end of Friday?

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.If we observe a change in the value of the variable equal to 2%,how does the estimate of the volatility change

Which of the following is true

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.What is the reversion rate for the variance rate implied by the model

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.What is the expected volatility in 20 days?

What does EWMA stand for?

Which of the following is true

How many parameters are necessary to define a GARCH (1,1)model

How many parameters are necessary to define an EWMA model

Introduction

Futures Markets and Central Counterparties

Hedging Strategies Using Futures

Interest Rates

Determination of Forward and Futures Prices

Interest Rate Futures

Swaps

Securitization and the Credit Crisis of 2007

Xvas

Mechanics of Options Markets

Properties of Stock Options

Trading Strategies Involving Options

Binomial Trees

Wiener Processes and Itos Lemma

The Black-Scholes-Merton Model

Employee Stock Options

Options on Stock Indices and Currencies

Futures Options and Blacks Model

The Greek Letters

Volatility Smiles

Basic Numerical Procedures

Value at Risk and Expected Shortfall

Credit Risk

Credit Derivatives

Exotic Options

Filters