Credit Risk Measurement and Management
Credit Risk Measurement and Management covers default probability, loss given default, exposure, portfolio credit risk, structural models, and credit derivatives. The exam tests both the arithmetic of expected loss and the reasoning behind spread and capital calculations.
Core rules
- Expected loss = PD × LGD × EAD. Unexpected loss is the volatility of loss and drives economic capital.
- Merton's structural model treats equity as a call on firm assets with strike equal to debt; default occurs when asset value falls below the debt barrier at maturity.
- Distance to default = [ln(V/D) + (μ − 0.5σ²)T]/(σ√T); PD = N(−DD).
- Credit spread ≈ PD × LGD over a one-period horizon; seniority and collateral reduce LGD and therefore the spread.
- CreditMetrics uses rating migration and transition matrices; netting and collateral reduce exposure; CVA prices counterparty credit risk into derivative marks.
- Wrong-way risk arises when exposure and counterparty credit quality are positively correlated.
Worked example
A bank has EAD of USD 20 million to a BBB borrower, one-year PD of 1.5%, and LGD of 45%. EL = 0.015 × 0.45 × 20,000,000 = USD 135,000. The implied fair credit spread is roughly PD × LGD = 0.675% = 67.5 bp, before liquidity premia and capital charges. Note that the EL is a provision-like expected cost; the spread must also compensate for unexpected loss.
Traps
- Multiplying PD by EAD and omitting LGD.
- Using real-world PD in pricing without adding a risk premium.
- Confusing distance to default with PD - they move in opposite directions.
- Treating senior securitization tranches as riskless when correlation and model error can erode them.