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# P2.T5.710. Bootstrap historical simulation and non-parametric density estimation (Dowd, Ch.4)

#### Nicole Seaman

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Learning objectives: Apply the bootstrap historical simulation approach to estimate coherent risk measures. Describe historical simulation using non-parametric density estimation.

Questions:

710.1. Betty is trying to decide between basic historical simulation (HS) and bootstrap historic simulation. In making her choice, which of the following statements is TRUE?

a. If she wants to avoid using a random number generator, then basic HS is better than bootstrap
b. If her primary goal is ease of implementation and ease of communication to the Risk Committee of the board of Directions--because she must conduct a presentation to the board on the method used--then basic HS is better than bootstrap
c. If her primary wish is that the generated VaR/HS are at least capable of exceeding the worst loss in the actual historical dataset, so that VaR/ES at least contemplates an outcome worse than has actually occurred in the recent past, then bootstrap is better than basic HS
d. If she wants to avoid the calculation of closed-form confidence interval around parameters--for example, if she wants to avoid using the chi-squared distribution to compute the confidence interval around variance--then bootstrap is better than basic HS

710.2. Which of the following is the chief drawback or limitation of the standard (aka, unmodified) bootstrap procedure?

a. Employs a random number which is too arbitrary
b. Difficult to compute standard errors of estimators
c. Presupposes observations are independent over time
d. Cannot be implement parametrically; i.e., requires a non-parametric dataset

710.3. According to Dowd, which of the following is the primary ADVANTAGE of non-parametric density estimation over basic historical simulation?

a. It is more straightforward
b. Kernel methods in particular produce superior estimates of VaR and ES in practice
c. It addresses some of the limitations and arbitrary judgments associated with the discontinuities of histograms
d. It allows us to fit familiar distribution (e.g., beta, gamma) to the data by using data to calibrate the familiar distribution's parameters