Credit Risk Measurement and Management
Structural versus reduced-form
Merton treats equity as a call option on firm assets struck at debt face value. Default occurs when asset value falls below the barrier at maturity. Distance to default is DD = [ln(V/D) + (mu - 0.5 sigma^2)T] / (sigma sqrt(T)), and PD = N(-DD). KMV/Edfi extends this empirically. Reduced-form models ignore the balance sheet and model default as a jump with hazard rate lambda; survival to T is exp(-lambda T), so cumulative PD = 1 - exp(-lambda T).
Loss building blocks
Expected loss = PD x LGD x EAD. Unexpected loss is the volatility of that loss and drives economic capital. Portfolio credit VaR depends on default correlation: higher correlation fattens the tail of the loss distribution even though it does not change expected loss. The Gaussian copula underlies CreditMetrics-style and CDO tranche pricing; correlation skew and tail dependence are the standard criticisms.
Counterparty and derivatives
CVA is the market value of counterparty credit risk and is subtracted from derivative value; DVA is the mirror image from the bank's own default. Wrong-way risk arises when exposure rises as counterparty quality falls.
Traps
Do not confuse distance to default (a scaled measure) with a probability. Distinguish physical PD from risk-neutral PD implied by spreads - risk-neutral PDs embed a risk premium and are higher. Remember that a tranche's attachment and detachment points define its exposure. Recovery assumptions and LGD given default are not the same as a market-implied recovery.
Worked example
Constant hazard rate of 2% per year. One-year PD = 1 - exp(-0.02) = 1.98%. Five-year PD = 1 - exp(-0.10) = 9.52%, not 10%.