Monte Carlo Simulation & VaR Flashcards

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

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.

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?

Answer: 100 paths

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

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

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.

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

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.

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

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.

In Monte Carlo simulation for interest rate risk, a mean-reverting process like Vasicek is preferred over GBM because:

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.

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?

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.