CRA Monte Carlo Simulation & VaR 3

Question 1

Which of the following best describes 'ghost features' or stale data problems in Historical Simulation VaR that Monte Carlo simulation avoids?

Accepted Answer

Scenarios from past crises permanently affecting the window

Answer

Historical Simulation uses a fixed rolling window, so extreme past events (e.g., the 2008 crisis) abruptly enter or exit the window, causing sudden VaR jumps — Monte Carlo avoids this by generating scenarios analytically.

Question 2

In a Monte Carlo simulation with 10,000 paths, at the 99% confidence level, how many paths represent the tail loss used to estimate VaR?

Accepted Answer

100 paths

Answer

At 99% confidence, the worst 1% of outcomes represent the tail — 1% of 10,000 paths equals 100 paths.

Question 3

A bank's Monte Carlo model uses geometric Brownian motion (GBM) for equity prices. Which real-world feature does GBM fail to capture?

Accepted Answer

Volatility clustering and fat tails

Answer

GBM assumes constant volatility and normally distributed returns, failing to capture the volatility clustering and heavy tails observed in actual market returns.

Question 4

The 'number of simulation runs' in Monte Carlo VaR most directly affects which property of the estimate?

Accepted Answer

Statistical precision (standard error) of the VaR estimate

Answer

More simulation runs reduce the standard error of the VaR estimate (standard error ∝ 1/√N), improving precision but not eliminating model bias.

Question 5

Which risk measure satisfies the property of sub-additivity, making it a 'coherent' risk measure unlike standard VaR?

Accepted Answer

Expected Shortfall (CVaR)

Answer

Expected Shortfall satisfies all four axioms of coherence (including sub-additivity), while VaR can violate sub-additivity for non-elliptical distributions.

(CRA) Certified Risk Analyst Practice Test

(CRA) Certified Risk Analyst Practice Test

CRA Monte Carlo Simulation & VaR 3