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What are the four axioms of a coherent risk measure, and how does VaR violate subadditivity?
A coherent risk measure must satisfy monotonicity, subadditivity, positive homogeneity, and translation invariance. VaR violates subadditivity because combining independent credit positions can increase measured VaR, contradicting the diversification principle.
How does variation margin work mechanically, and how does it differ from initial margin in terms of purpose and daily operations?
Variation margin settles daily mark-to-market changes by exchanging cash between counterparties. Unlike initial margin (which covers future exposure), VM addresses realized gains and losses. The process runs daily with calls subject to MTA thresholds and dispute resolution procedures.
What is the multi-curve framework, and why did the 2008 crisis force a separation between discounting and forward projection curves?
The multi-curve framework uses separate curves for discounting (OIS/risk-free) and forward rate projection (tenor-specific). The 2008 crisis forced this separation when LIBOR-OIS spreads widened to 350+ basis points, proving that LIBOR was not risk-free.
How do cliquet options accumulate returns through their reset mechanism, and why are they popular in structured products?
Cliquet options are a series of forward-starting options that reset the strike to the current spot at each period. Returns are capped and floored per period, then accumulated, making them popular in structured products that offer principal protection with equity participation.
What are the NGFS climate scenarios, and how do banks use them for transition risk assessment?
The NGFS provides six standardized climate scenarios ranging from orderly transition to hot house world. Banks use these to stress-test portfolios by mapping carbon-sensitive exposures, applying scenario-specific carbon price trajectories, and translating impacts into credit metrics like PD and expected losses.
What is the Incremental Risk Charge (IRC), and how does it capture default and migration risk in the trading book?
The Incremental Risk Charge captures default and migration risk for credit-sensitive trading book positions over a 1-year horizon at 99.9% confidence. It assumes a constant level of risk through periodic rebalancing. Under FRTB, the IRC is replaced by the Default Risk Charge.
How does the Internal Models Approach (IMA) for market risk capital work under the FRTB framework?
Under FRTB, the Internal Models Approach calculates market risk capital as the sum of an Expected Shortfall component (with varying liquidity horizons), a Default Risk Charge, and a Stressed Capital Add-On for non-modellable factors. Approval is granted at the individual trading desk level.
What are the trade reporting requirements for OTC derivatives under Dodd-Frank and EMIR, and what role do swap data repositories play?
Trade reporting mandates require all OTC derivative transactions to be reported to registered repositories. Under Dodd-Frank, reporting is one-sided based on a hierarchy, while EMIR requires dual-sided reporting by both counterparties within T+1.
How does central clearing of OTC derivatives work, and what role does a CCP play in reducing counterparty risk?
Central clearing interposes a CCP between the original buyer and seller of an OTC derivative. The CCP manages risk through initial margin, variation margin, and a structured default waterfall. While clearing reduces bilateral counterparty risk, it concentrates systemic risk in the CCP.
What is 'significant risk transfer' in securitization and why does it matter for capital relief?
Significant Risk Transfer is the regulatory test determining whether a bank securitization achieves capital relief. The bank must demonstrate that genuine risk has been transferred to investors through quantitative loss-sharing tests and qualitative checks for implicit support.
How do heating degree days and cooling degree days work in weather derivatives?
Weather derivatives allow businesses to hedge revenue exposure to temperature fluctuations. Heating Degree Days (HDD) measure cold relative to a 65°F baseline, while Cooling Degree Days (CDD) measure heat above it. Contracts typically cover a cumulative period.
Why is backtesting expected shortfall (ES) so much harder than backtesting VaR?
The shift from VaR to expected shortfall (ES) in the FRTB introduced a significant practical challenge: ES is much harder to backtest than VaR. This tension is a key topic in FRM Part II.
How does Black's model for options on futures differ from the standard Black-Scholes model?
Black's model (1976) is essentially Black-Scholes adapted for options where the underlying is a futures contract rather than a spot asset. The key simplification is that the futures price already incorporates the cost of carry.
What are the financial stability implications of Central Bank Digital Currencies (CBDCs), and what risks should banks prepare for?
Central Bank Digital Currencies introduce significant financial stability risks, primarily through deposit disintermediation — households shifting funds from commercial bank deposits to risk-free central bank digital money. This raises funding costs, amplifies digital bank run risk, and alters monetary policy transmission.
How does ISDA SIMM calculate initial margin for non-cleared derivatives, and what are the key risk buckets?
ISDA SIMM is the industry-standard sensitivity-based method for calculating initial margin on bilateral non-cleared OTC derivatives. It computes delta, vega, and curvature sensitivities across six risk classes, applies prescribed risk weights, and aggregates using a correlation-based framework.
How do AIC and BIC work for comparing risk models, and when would they give different recommendations?
AIC and BIC both balance goodness-of-fit against model complexity, but BIC penalizes additional parameters more heavily, especially for large samples. AIC tends to prefer slightly more complex models while BIC favors parsimony.
What is asset-backed commercial paper (ABCP) and what liquidity risks do ABCP conduits face?
Asset-backed commercial paper (ABCP) is short-term debt typically maturing in 30-90 days, issued by a special purpose vehicle called a conduit and backed by longer-term financial assets. The fundamental risk lies in the maturity transformation between short-term funding and long-term assets.
How does Extreme Value Theory (EVT) improve tail risk estimation, and what is the Peaks-over-Threshold approach?
EVT models only the extreme tail of the return distribution using the Generalized Pareto Distribution. The Peaks-over-Threshold method fits exceedances above a high threshold, providing theoretically justified tail risk estimates far more accurate than Normal or Student-t.
What determines loss given default (LGD), and how do workout LGD and market LGD differ?
LGD depends on seniority, collateral, industry, economic conditions, and jurisdiction. Workout LGD tracks actual recovery cash flows over years, while market LGD uses post-default trading prices for quick estimation.
What is volatility clustering and how do you test for ARCH effects in financial returns?
Volatility clustering means large price moves tend to follow large moves. The Engle LM test detects ARCH effects by regressing squared residuals on their lags — a significant test statistic means volatility is time-varying.
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