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How do Eurodollar futures work mechanically, and how does a corporate treasurer use them to lock in a borrowing rate?
Eurodollar futures were among the most liquid interest rate derivatives ever created. The futures price is quoted as 100 minus the annualized rate, with each basis point worth $25 per contract. Here is a step-by-step hedging example for a corporate borrower.
How do netting agreements reduce counterparty exposure and how is netting set exposure calculated?
A netting set is a group of trades with the same counterparty under a single master netting agreement. Netting allows you to offset positive and negative MTM values, dramatically reducing counterparty exposure compared to gross exposure calculation.
How do you construct the loss distribution for a credit portfolio, and what is the difference between expected and unexpected loss?
Building the credit portfolio loss distribution is the core challenge of credit risk management. Expected loss is straightforward to compute; the difficulty lies in capturing how losses cluster due to default correlations.
How do you value an interest rate swap that is already partway through its life?
Valuing an interest rate swap mid-life is one of the most testable skills in FRM Part I. The key insight is that a swap can be decomposed into two legs, and you value each leg separately using current market discount factors.
What makes a risk measure 'coherent,' and why does Expected Shortfall satisfy the criteria while VaR does not?
A coherent risk measure satisfies four axioms: monotonicity, subadditivity, positive homogeneity, and translation invariance. VaR fails subadditivity — combining portfolios can paradoxically increase measured risk — while Expected Shortfall satisfies all four axioms.
How does the Vasicek single-factor model work for credit portfolio loss estimation, and what is the granularity adjustment?
The Vasicek single-factor model is the theoretical foundation for Basel's IRB capital formula. It models each obligor's default as depending on a common systematic factor and an idiosyncratic factor, producing a portfolio loss distribution that captures correlated defaults during economic downturns.
How is logistic regression used for predicting loan defaults, and how do you interpret the coefficients?
Logistic regression is the workhorse model for binary credit outcomes because it maps any combination of inputs to a probability bounded between 0 and 1. Instead of modeling default probability directly, it models the log-odds as a linear function.
How does the cheapest-to-deliver (CTD) bond work in Treasury futures, and why does it matter for hedging?
Treasury futures allow the short side to deliver any bond from a basket of eligible maturities, but naturally they will choose the one that minimizes their cost. This is the cheapest-to-deliver (CTD) bond. The exchange assigns each deliverable bond a conversion factor that adjusts its price as though it yielded exactly 6%.
What is component VaR and how does it decompose portfolio risk?
Component VaR decomposes total portfolio VaR into additive contributions from each position: CVaRᵢ = βᵢ × wᵢ × Portfolio VaR. Unlike individual VaRs, component VaRs sum exactly to portfolio VaR, revealing which positions contribute most to risk.
What are the main credit risk mitigation techniques and how do they reduce exposure?
Credit risk mitigation techniques include collateral (reduces LGD/EAD), netting (reduces gross exposure), guarantees (substitutes the guarantor's credit quality), and credit enhancements (subordination, overcollateralization). Basel recognizes specific CRM techniques for regulatory capital relief.
What is kernel density estimation and when is it preferred over histograms?
Kernel density estimation (KDE) creates a smooth probability density estimate by placing a kernel (usually Gaussian) on each data point and summing them. Unlike histograms, KDE is not dependent on arbitrary bin choices. The bandwidth parameter controls the smoothness.
How do repo haircuts work and what determines their size?
A repo haircut is the percentage difference between collateral market value and cash lent, protecting the lender against collateral value declines. Haircuts range from 0.5% for Treasuries to 25%+ for equities, and they increase procyclically during crises.
What are the main credit scoring model approaches and how does logistic regression compare to machine learning methods?
Credit scoring models assign a numerical score representing the probability that a borrower will default. There are several major approaches including logistic regression, decision trees, and neural networks, each with distinct trade-offs in accuracy versus interpretability.
What are the main pitfalls of historical simulation VaR and how do ghost effects distort results?
Historical simulation VaR has several pitfalls: the ghost effect (VaR jumps when extreme observations enter/exit the rolling window), inability to extrapolate beyond the worst historical loss, slow reaction to regime changes due to equal weighting, and regime dependence. Filtered HS and age-weighted approaches mitigate these issues.
How does the KMV model improve on Merton, and what is the Expected Default Frequency?
The KMV model improves on Merton by using an empirical default point (short-term debt plus half of long-term debt) and mapping distance to default to actual default frequencies from a historical database rather than the theoretical normal distribution, which systematically underestimates defaults.
How does the EWMA volatility model work and how do I choose the lambda parameter?
The EWMA volatility model estimates today's variance as a weighted average of yesterday's variance and yesterday's squared return, with lambda controlling the decay rate. RiskMetrics standardized lambda at 0.94 for daily data, giving an effective window of about 17 days.
How do Eurodollar futures differ from Treasury futures when hedging interest rate exposure?
Eurodollar futures are based on the 3-month SOFR rate and hedge short-term funding costs, while Treasury bond futures deliver actual bonds and hedge longer-duration portfolios. The key distinction involves settlement mechanics, duration exposure, and convexity bias.
Under FRTB, how does a bank decide between the Standardized Approach and Internal Models Approach for market risk capital?
Under FRTB, the choice between Standardized and Internal Models Approach is made at the trading desk level. Each desk must pass regulatory approval, P&L attribution testing, and backtesting to qualify for IMA. Desks that fail any gate must use the Standardized Approach.
What is wrong-way risk in counterparty credit, and why does it make standard CVA models underestimate losses?
Wrong-way risk occurs when your exposure to a counterparty increases at the same time their credit quality deteriorates. This positive correlation means standard CVA models that assume independence between exposure and default probability will systematically underestimate losses.
How do you calculate Expected Loss from PD, LGD, and EAD, and why does each component matter separately?
Understanding the three pillars of expected loss is essential for FRM Part II credit risk. Banks estimate PD, LGD, and EAD independently because each is driven by different factors: PD reflects borrower creditworthiness, LGD depends on collateral and seniority, and EAD accounts for potential drawdowns on revolving facilities.
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