qingshu

 

AIM 3: Discuss the implications regime switching has on quantifying volatility.

A regime-switching volatility model of interest rates would assume all of the following EXCEPT:

A) the regime determines whether the volatility of interest rates is high or low.

B) the unconditional distribution of interest rates is normally distributed.

C) the mean is constant.

D) interest rates are conditionally normally distributed.

qingshu

 

The correct answer is B

A regime-switching volatility model assumes different market regimes exist with high or low volatility.  The mean is assumed constant, but the volatility depends on the regime.  Conditional on the fact that interest rates are drawn from one regime, the distribution is normally distributed.  If interest rates are drawn from more than one regime, this unconditional distribution need not be normally distributed.

qingshu

 

AIM 5: Compare and contrast parametric approaches for estimating conditional volatility, including the historical standard deviation approach, the RiskMetrics? approach and the GARCH approach, and discuss the advantages and disadvantages of nonparametric methods for volatility forecasting.

1、

λ = 0.97 K = 150
Rank	Ten Lowest Returns	Number of Past Periods	Hybrid Weight	Hybrid Cumulative Weight
1	–4.10%	5	0.0268	0.0268
2	–3.80%	7	0.0253	0.0521
3	–3.50%	21	0.0165	0.0686
4	–3.20%	13	0.0210	0.0896
5	–3.10%	28	0.0133	0.1029
6	–2.90%	55	0.0059	0.1088
7	–2.80%	28	0.0133	0.1221
8	–2.60%	28	0.0133	0.1354
9	–2.55%	28	0.0133	0.1487
10	–2.40%	55	0.0059	0.1546

The VAR measure for the fifth percentile using the historical simulation approach is closest to:

A)  –3.90%.

B)  –2.70%.

C)  –3.80%.

D)  –3.10%.

qingshu

 

The correct answer is B

Under the historical simulation approach, all returns in the estimation window are equally weighted. In this example, K = 150; therefore, each return has a weight of 1 / 150 = .666667%, as shown in the following table. The fifth percentile is somewhere between –2.80% and –2.60%. The midpoint –2.70% has a cumulative weight of 5.00% (5.00% = (4.67% + 5.33%) / 2). If the midpoint did not have a cumulative weight of exactly 5.00%, interpolation would be necessary to find the fifth percentile.

Ten Lowest Returns	Historical Simulation Weight	HS Cumulative Weight
–4.10%	0.00666667	0.0067
–3.80%	0.00666667	0.0133
–3.50%	0.00666667	0.0200
–3.20%	0.00666667	0.0267
–3.10%	0.00666667	0.0333
–2.90%	0.00666667	0.0400
–2.80%	0.00666667	0.0467
–2.60%	0.00666667	0.0533
–2.55%	0.00666667	0.0600
–2.40%	0.00666667	0.0667

 

qingshu

 

2、The VAR measure for the fifth percentile using the hybrid approach is closest to:

A) –3.82%.

B) –4.10%.

C) –3.80%.

D) –3.10%.

qingshu

 

The correct answer is

The lowest and second lowest returns have cumulative weights of 2.68% and 5.21%, respectively. The point halfway between the two lowest returns is interpolated as –3.95% with a cumulative weight of 3.945%, calculated as follows: (2.68% + 5.21%) / 2. Further interpolation is required to find the fifth percentile VAR level with a return somewhere between –3.80% and –3.95%. The 5 percent VAR using the hybrid approach is calculated as:

3.95% – (3.95% – 3.80%)[(0.05 – 0.03945) / (0.0521 – 0.03945)] = 3.95% – 0.15%[0.8340] = 3.8249%

Notice that the answer has to be between –3.8% and –3.95%, so –3.82 is the only possible answer.

qingshu

 

3、Which of the following approaches is the most restrictive regarding the underlying assumption of the asset return distribution?

A) nonparametric.

B) parametric.

C) hybrid.

D) multivariate density estimation.

qingshu

 

The correct answer is B

A parametric model typically assumes asset returns are normally or lognormally distributed with time-varying volatility. The other approaches do not require assumptions regarding the underlying asset return distribution.

qingshu

 

4、Which of the following derivative instruments could be classified as linear or approximately linear?

I.           Swaption

II.         Forward on commodity

III.        Interest rate cap

IV.      Futures on equity index

V.        Currency swap

A) II and IV.

B) I and III.

C) II, IV, and V.

D) II, III, and IV.

qingshu

 

The correct answer is C

The value of a linear derivative has a constant linear relationship with the underlying asset.  The relationship does not need to be one-to-one but it must be constant (or approximately constant) and linear.  Forwards, futures, and swaps are generally linear.  The value of a nonlinear derivative is a function of the change in the underlying asset and depends on the state of the underlying asset.  Options generally are nonlinear.