qingshu

 

5、The historical standard deviation approach differs from the RiskMetricsTM and GARCH approaches for estimating conditional volatility, because it:

A) is a parametric method.

B) places a lower weight on more recent data.

C) uses recent historical data.

D) applies a set of weights to past squared returns.

qingshu

 

The correct answer is B

All three methods are parametric, use historical data, and apply weights to past squared returns. The historical standard deviation approach weighs all returns in the estimation window equally. The RiskMetricsTM and GARCH approaches are exponential smoothing approaches that place a higher weight on more recent data.

qingshu

 

6、Which of the following statements regarding volatility in VAR models are TRUE? I. The RiskMetricsTM approach is very similar to the GARCH model. II. The historical standard deviation approach creates a variance-covariance matrix that is estimated under the assumption that all asset returns are normally distributed. III. The parametric approach typically assumes asset returns are normally or lognormally distributed with constant volatility. IV. Exponential smoothing methods and the historical standard deviation methods both apply a set of weights to recent past squared returns.

A) I, III, and IV.

B) I, II, and III.

C) I, II, and IV. 

D) II, III, and IV.

qingshu

 

The correct answer is C

The third statement is false. The parametric approach typically assumes asset returns are normally or lognormally distributed with time-varying volatility. The RiskMetricsTM approach is actually a special case of the GARCH model. Both the exponential and historical standard deviation approaches create a variance-covariance matrix that is estimated under the assumption that all asset returns are normally distributed. Exponential smoothing methods and the historical standard deviation methods both apply a set of weights to recent past squared returns. The difference is that in the historical standard deviation method all weights are equal whereas more recent returns are weighted more heavily in exponential methods.

qingshu

 

7、Which of the following is/are (an) advantage(s) of nonparametric methods compared to parametric methods for quantifying volatility? I. Nonparametric models require assumptions regarding the entire distribution of returns. II. Data is used more efficiently with nonparametric methods than parametric methods. III. Fat tails, skewness and other deviations from some assumed distribution are no longer a concern in the estimation process for nonparametric methods. IV. Multivariate density estimation (MDE) allows for weights to vary based on how relevant the data is to the current market environment by weighting the most recent data more heavily.

A) I and II.

B) I and III.

C) III only.

D) III and IV.

qingshu

 

The correct answer is C

Fat tails, skewness, and other deviations from some assumed distribution are no longer a concern in the estimation process for nonparametric methods. The other statements are false for the following reasons. Nonparametric models do not require assumptions regarding the entire distribution of returns. Data is used more efficiently with parametric methods than nonparametric methods. Multivariate density estimation (MDE) allows for weights to vary based on how relevant the data is to the current market environment, regardless of the timing of the most relevant data. MDE is also very flexible in introducing dependence on state variables.

qingshu

 

8、Consider the following four GARCH equations:

Equation 1: σ2n = 0.83 + 0.05μ2n-1 + 0.93σ2n-1

Equation 2: σ2n = 0.06 + 0.04μ2n-1 + 0.95σ2n-1

Equation 3: σ2n = 0.60 + 0.10μ2n-1 + 0.94σ2n-1

Equation 4: σ2n = 0.03 + 0.03μ2n-1 + 0.93σ2n-1

Which of the following statements regarding these equations is (are) CORRECT?

I.Equation 1 is a stationary model.

II.Equation 2 shows no mean reversion

III.Volatility will revert to a long run mean level faster with Equation 1 than it will for Equation 4.

IV.Volatility will revert to a long run mean level faster with Equation 3 than it will for Equation 2.

A) I only.

B) III only.

C) II and III only.

D) II and IV only.

qingshu

 

The correct answer is A

The format of the GARCH equation is σ2n = ω + αμ2n-1 + βσ2n-1, where (α + β) = persistence. For a model to be stationary over time, the persistence must be less than one. A persistence of one means there is no mean reversion and the higher the persistence, the longer it will take for volatility to revert to a long run mean level following a large shock or movement. The persistence for Equation 2 is (0.04 + 0.95) = 0.99, which is less than one meaning there is mean reversion. The persistence for Equation 1 is higher than that of Equation 3, meaning mean reversion will take longer for Equation 1. Because the persistence for Equation 1 is less than one, Equation 1 is a stationary model. Equation 3 has a persistence greater than one, which mean the model shows no mean reversion. Only Statement III is correct.

qingshu

 

9、GARCH(1,1) (generalized autoregressive conditional heteroskedastic) models of volatility may be useful for option traders because they:

A) provide efficient estimates of past volatility.

B) are useful in forecasting future volatility

C) are the simplest volatility models to estimate.

D) are used in the Black-Scholes option pricing model.

qingshu

 

The correct answer is B

GARCH(1,1) models have been shown to be useful in forecasting future volatility, which may indicate to an option trader the relative value of an option price.