Financial Risk Modeling & Quantitative Analysis Flashcards

A portfolio has a delta of 500 and a gamma of 20 with respect to an underlying asset. If the asset price moves +$2, what is the approximate change in portfolio value using a second-order Taylor expansion?

Answer: $1,040

ΔV ≈ δ × ΔS + ½ × γ × (ΔS)² = 500×2 + ½×20×4 = 1,000 + 40 = $1,040.

What is the purpose of stress testing in financial risk management that distinguishes it from VaR?

Answer: Stress testing evaluates portfolio impact under specific severe but plausible scenarios, not statistical confidence intervals

Unlike VaR, which estimates losses at a statistical quantile, stress testing applies specific hypothetical or historical shock scenarios to assess vulnerability to severe events.

In the Merton structural credit model, a firm defaults when its asset value falls below which level at debt maturity?

Answer: The face value of its debt (the default barrier)

In Merton's model, default occurs if asset value V_T < D (face value of debt) at maturity T, treating equity as a call option on firm assets.

Which technique is used to reduce variance in Monte Carlo simulations by pairing each random sample with its antithetic counterpart?

Answer: Antithetic variates

Antithetic variates use both a random draw u and (1−u) as paired scenarios, exploiting negative correlation to reduce the variance of the estimator.

What does a positive skewness coefficient in a return distribution imply about tail risk for a short-position holder?

Answer: The right tail is fatter, meaning large positive returns (losses for the short holder) are more frequent than the normal distribution predicts

Positive skewness means the distribution has a longer right tail; for a short seller, large positive moves in the underlying are losses, so positive skewness increases their tail risk.

A risk manager computes correlation between two assets as 0.85 using historical data. Which issue should they be most concerned about when using this in a VaR model during a crisis?

Answer: Correlation breakdown — correlations tend to spike toward 1 during market stress, making diversification benefits disappear

Empirical evidence shows that cross-asset correlations rise sharply during crises (contagion), invalidating the assumption of stable correlations embedded in normal-period estimates.

What does the term 'wrong-way risk' refer to in counterparty credit risk?

Answer: The adverse situation where the counterparty's likelihood of default increases as the exposure to that counterparty also increases

Wrong-way risk arises when the credit quality of a counterparty is negatively correlated with the market value of the trade, worsening both exposure and default probability simultaneously.