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P2.T7.506. Model error (Malz)

Nicole Seaman

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Learning outcomes: Describe ways that errors can be introduced into models. Describe how horizon, computational and modeling decisions can impact VaR estimates.

Questions:

504.1. In finance, a standard model of the behavior over time of an asset price or risk factoris the geometric Brownian motion (or diffusion model) This model is also the basis for the Black-Scholes option pricing model, and is generally a point of departure for analysis of asset return behavior. In this standard model, returns are normally distributed. However, it is well understood that actual returns do not necessarily comport to the standard model. In fact, teal-world asset returns tend to exhibit each of the following EXCEPT for which is not generally true about real-world asset returns?

a. Leptokurtosis
b. The distributional mean differs from the median
c. 45-degree QQ-plot and low Jarque-Bera value
d. Time variation


504.2. Each of the following is true about value at risk (VaR) EXCEPT which is false?

a. VaR cannot be backtested
b. VaR cannot rank portfolios in order of riskiness
c. VaR cannot provide powerful tests of its own accuracy
d. Dramatic changes in VaR can be obtained by subtle differences in its parameters. ("Subtle differences in how VaR is computed can lead to large differences in the estimates")


504.3. Consider the following four statements about value at risk (VaR):

I. If there were standardization of both the confidence interval and the time horizon, VaR estimates would be highly consistent across users
II. There is not much uniformity of practice as to confidence interval and time horizon; as a result, intuition on what constitutes a large or small VaR is underdeveloped.
III. There are a number of computational and modeling decisions that can greatly influence VaR results, such as the length of time series used for historical simulation or to estimate moments; and the technique used for estimating moments
IV. There are a number of computational and modeling decisions that can greatly influence VaR results, such as mapping techniques and the choice of risk factors

Which of the above statements is (are) true?

a. None are true
b. I. and II. are true
c. II., III. and IV. are true
d. All are true

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