Financial Risk Modeling & Quantitative Analysis Flashcards

A bank's internal model back-test produces 12 exceptions over 250 trading days at 99% VaR. Under Basel traffic light rules, which zone does this fall into?

Answer: Red zone (capital multiplier increase required)

Basel traffic light rules place 10 or more exceptions in the red zone, triggering mandatory increases to the capital multiplier for market risk.

Which risk measure satisfies all four axioms of coherence (translation invariance, subadditivity, positive homogeneity, and monotonicity)?

Answer: Expected Shortfall

Expected Shortfall is a coherent risk measure; VaR famously violates subadditivity, meaning diversification can appear to increase risk when measured by VaR.

In credit risk modeling, what does the asset correlation parameter ρ control in the Vasicek single-factor model?

Answer: The sensitivity of an obligor's asset returns to the common systematic factor

In the Vasicek model, ρ determines how much of an obligor's asset value movements are driven by the shared market factor versus idiosyncratic shocks.

A risk analyst computes a 1-day 99% parametric VaR of $2M. After applying a liquidity-adjusted horizon of 10 days, what is the adjusted VaR assuming i.i.d. returns?

Answer: $6.32M

Scaling by √10 gives $2M × √10 ≈ $2M × 3.162 = $6.32M under the square-root-of-time assumption.

What is the primary limitation of Historical Simulation for computing VaR?

Answer: It relies entirely on past data and cannot account for unprecedented market conditions

Historical Simulation uses actual past returns as scenarios, so it cannot capture tail risks from events that have not occurred in the historical window.

Which test is commonly used to assess whether a time series of financial returns exhibits autoregressive conditional heteroskedasticity (ARCH effects)?

Answer: Engle's ARCH-LM test

Engle's Lagrange Multiplier test regresses squared residuals on lagged squared residuals to detect clustering of variance, the hallmark of ARCH effects.

In extreme value theory (EVT), the Peaks Over Threshold (POT) method models tail losses using which distribution?

Answer: Generalized Pareto Distribution (GPD)

The POT method fits a Generalized Pareto Distribution to exceedances above a chosen high threshold, providing a theoretically justified model for the tail.