[2008] Topic 11: Value at Risk 相关习题 price, normal, method, actual

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AIM 1: Distinguish Between Monte Carlo simulation and bootstrapping.

1、The Monte Carlo estimation of VAR:

A) is based on a normal distribution.

B) uses historical data.

C) is based on actual asset price data.

D) is also known as the delta-normal method.

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The correct answer is A

Monte Carlo simulation involves the creation of a distribution of pricing paths given randomly generated data. It is accomplished by taking samples from a normal distribution to create distributions of potential future outcomes. For every future outcome (or scenario), a portfolio value can be generated and a corresponding value at risk measure can be estimated.

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2、The bootstrapping technique of VAR:

A) is based on a normal distribution.

B) uses historical data.

C) requires lenghty computation time.

D) creates pricing paths.

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The correct answer is B

Bootstrapping estimation, on the other hand, utilizes historical data to estimate future outcomes. Both methods use one of two procedures: (1) a single-step procedure and long-term data; this procedure is used when the data has the same time scale as the time horizon of interest, or (2) a multi-step procedure and short-term data to create longer term periods.

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3、Which of the following statement about bootstrapping is TRUE?

A) Bootstrapping requires the time scale of the data to be equal to the time scale of interest.

B) Bootstrapping is one method for estimating VaR.

C) Bootstrapping requires a distributional assumption about the data.

D) Bootstrapping uses simulated data to estimate future outcomes.

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The correct answer is B

No distributional assumptions are needed to implement bootstrapping. Bootstrapping attempts to use historical data to estimate the future.

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AIM 2: Describe the implementation of Monte Carlo simulation for VAR calculations.

VaR is a commonly used risk metric. Typically VaR is estimated via a Monte Carlo simulation or via a bootstrapping method. Implementation of the Monte Carlo simulation for VaR includes all of the following EXCEPT:

I.           first a distribution is selected from common statistical methods.

II.         samples are made from a Normal distribution and used to build a distribution of future events.

III.        hyperparameters are then inserted into the estimation model.

IV.      for each event a pricing model is used to determine asset/portfolio values and then approximate VaR.

A) II and IV only.

B) I only.

C) I, II, III, and IV.

D) I and III only.

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The correct answer is D

Statement I is incorrect. Random numbers are generated. Statement III is incorrect. Models need not be hierarchical in nature.

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AIM 3: Identify the distribution of maxima and minima.

1、Which of the following statements about extreme value theory (EVT) is FALSE?

A) EVT can be used to model everyday occurrences. 

B) Cluster analysis is appropriate for financial data with time dependency. 

C) POT models determine the cut-off between typical and extreme values. 

D) EVT focuses on data that is generally considered outliers.

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The correct answer is A

EVT models are appropriate for low probability, high impact events; not everyday occurrences.