CRA Monte Carlo Simulation & VaR 3 — Questions and Answers
Question 1: Which of the following best describes 'ghost features' or stale data problems in Historical Simulation VaR that Monte Carlo simulation avoids?
- Over-reliance on derivatives pricing models
- Scenarios from past crises permanently affecting the window (Correct answer)
- Use of correlated random number generators
- Inability to model non-linear instruments
Correct answer: Scenarios from past crises permanently affecting the window
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?
- 10 paths
- 100 paths (Correct answer)
- 1,000 paths
- 9,900 paths
Correct answer: 100 paths
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?
- Continuous price changes
- Volatility clustering and fat tails (Correct answer)
- Positive drift in equity prices
- Random walk behavior
Correct answer: Volatility clustering and fat tails
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?
- Bias of the VaR estimate
- Statistical precision (standard error) of the VaR estimate (Correct answer)
- The confidence level used
- The holding period assumption
Correct answer: Statistical precision (standard error) of the VaR estimate
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?
- Parametric VaR
- Historical VaR
- Expected Shortfall (CVaR) (Correct answer)
- Stressed VaR
Correct answer: Expected Shortfall (CVaR)
Expected Shortfall satisfies all four axioms of coherence (including sub-additivity), while VaR can violate sub-additivity for non-elliptical distributions.
Question 6: In Monte Carlo simulation for interest rate risk, a mean-reverting process like Vasicek is preferred over GBM because:
- Interest rates can be negative under GBM
- Interest rates tend to revert to a long-run mean, unlike equity prices (Correct answer)
- GBM cannot model multi-currency portfolios
- Vasicek produces fatter tails than GBM
Correct answer: Interest rates tend to revert to a long-run mean, unlike equity prices
Unlike equity prices, interest rates exhibit mean reversion toward a long-run equilibrium level, which the Vasicek and CIR models explicitly capture.
Question 7: A portfolio manager uses a copula in Monte Carlo VaR to model the dependence structure between assets. What does a Gaussian copula fail to capture compared to a t-copula?
- Linear correlation between assets
- Tail dependence during market stress (Correct answer)
- Portfolio-level diversification benefits
- Individual asset volatility
Correct answer: Tail dependence during market stress
The Gaussian copula implies zero tail dependence, meaning extreme joint losses appear less likely than observed in real markets; the t-copula captures positive tail dependence.
CRA Monte Carlo Simulation & VaR 3
Which of the following best describes 'ghost features' or stale data problems in Historical Simulation VaR that Monte Carlo simulation avoids?