Credit Risk & Credit Derivatives

The yield difference between a defaultable bond and a risk-free bond of identical maturity and currency. To first order it compensates for expected loss: spread ≈ PD × LGD (under risk-neutral measure).

Recovery rate R is the fraction of notional recovered after default. Loss given default is LGD = 1 − R. Both are expressed under the relevant measure (historical or risk-neutral) and conventions (face vs. market).

The probability that an obligor defaults within a given horizon. Real-world (physical) PDs come from rating/transition data; risk-neutral PDs are extracted from market prices (bonds, CDS) and are typically larger because they embed risk premia.

EL = PD × LGD × EAD, where EAD is exposure at default. This is the building block of credit pricing, IRB capital, and provisions (IFRS 9 / CECL).

A firm's equity is a European call option on its asset value Vₜ with strike equal to the face of debt D, maturing at T. Default occurs if V_T < D. Equity value E₀ = BSCall(V₀, D, T, σ_V, r).

Under the Merton model, risk-neutral PD = N(−d₂) with d₂ = [ln(V₀/D) + (r − ½σ_V²)T] / (σ_V √T). Equivalently, PD = N(−DD) where DD is distance to default.