Financial Risk Modeling & Quantitative Analysis Flashcards

Which method for computing VaR explicitly accounts for fat tails by fitting a parametric distribution with degrees-of-freedom parameter ν?

Answer: Parametric VaR using Student's t-distribution

The Student's t-distribution with low degrees of freedom produces heavier tails than the normal, making it a better parametric fit for financial return distributions with excess kurtosis.

In risk factor mapping, why are bonds mapped to standard maturity vertices rather than their exact cash flow dates?

Answer: To reduce the number of risk factors and enable VaR computation from a manageable covariance matrix

Mapping cash flows to standard vertices (e.g., 1M, 3M, 1Y, 2Y…) reduces thousands of unique payment dates to a small set of common risk factors for which a covariance matrix can be estimated.

A credit portfolio manager observes that individual loan PDs are 2% but the portfolio loss distribution has a much fatter tail than a binomial model predicts. What most likely explains this?

Answer: Positive default correlation among borrowers driven by common macroeconomic factors

When defaults are correlated due to shared economic exposures, the loss distribution becomes skewed with a heavier tail than implied by independent binomial defaults.

What is the role of the 'economic capital' concept in financial risk management?

Answer: It is the capital buffer a firm holds to absorb unexpected losses at a given confidence level over a defined horizon

Economic capital is an internal measure of the capital needed to remain solvent against unexpected losses at a specified confidence level (e.g., 99.9%), independent of regulatory minimums.

Which numerical technique is best suited for pricing path-dependent options (e.g., Asian options) where closed-form solutions do not exist?

Answer: Monte Carlo simulation

Monte Carlo simulation generates thousands of asset price paths and averages payoffs, making it ideal for path-dependent products whose payoff depends on the entire price trajectory.

A risk model produces a Kupiec LR test statistic of 6.5 with 1 degree of freedom. At the 5% significance level (critical value ≈ 3.84), what conclusion is drawn?

Answer: Reject the null hypothesis; the model's VaR is mis-specified

Since 6.5 > 3.84, the test statistic exceeds the critical value, leading to rejection of H₀ that the observed exception rate equals the nominal tail probability.

What distinguishes 'model risk' from 'parameter estimation risk' in quantitative finance?

Answer: Model risk arises from using the wrong mathematical framework, while parameter estimation risk stems from imprecise calibration of a correct model

Model risk is the risk that the chosen model structure is fundamentally wrong (e.g., assuming normality when fat tails exist), while estimation risk reflects statistical uncertainty in fitting a structurally correct model.