A credit derivative transfers credit risk without transferring the underlying asset. The buyer pays a periodic premium; the seller pays out if a credit event occurs. Mispricing these instruments was central to the 2008 financial crisis.
Credit default swap pricing
A CDS is insurance on a bond. The protection buyer pays a periodic spread s (in basis points per year) on the notional. If the reference entity defaults, the seller pays (1 − R) × notional, where R is the recovery rate. The fair spread equates the present value of premium payments to the present value of the contingent leg.
A collateralized debt obligation pools credit-risky assets and slices cash flows into tranches. The equity tranche absorbs first losses (highest yield, highest risk). The mezzanine takes losses after equity is wiped out. The senior tranche is last to lose and is often rated AAA. Correlation between defaults is the key parameter: higher correlation means the senior tranche is riskier than its rating suggests.
Counterparty risk is the risk that the protection seller cannot pay when the credit event occurs. This creates wrong-way risk: the seller is most likely to default exactly when the protection is needed most, because systemic stress hits everyone. The credit valuation adjustment (CVA) prices this risk into the derivative.
The crisis revealed three failures: (1) Gaussian copula models underestimated default correlation, treating tail events as nearly impossible. (2) Rating agencies applied the same AAA label to CDO tranches and sovereign debt, despite fundamentally different risk profiles. (3) Concentration of counterparty risk at AIG meant that when AIG was rescued by the U.S. government in September 2008, it exposed how a single institution's failure could have cascaded through the system. The lesson: model risk is itself a systemic risk.
Scheme
; Correlation sensitivity: how default correlation; affects the probability of catastrophic losses; Binomial model: n independent bonds, each with PD p; P(k defaults) with independence assumption
(define (factorial n)
(if (<= n 1) 1 (* n (factorial (- n 1)))))
(define (choose n k)
(/ (factorial n) (* (factorial k) (factorial (- n k)))))
(define (binom-prob n k p)
(* (choose n k)
(expt p k)
(expt (- 1 p) (- n k))))
; 100-bond pool, 5% individual PD; P(10+ defaults) under independence
(define (prob-at-least-k n k p)
(let loop ((j k) (total 0))
(if (> j n) total
(loop (+ j 1) (+ total (binom-prob n j p))))))
(define p-tail (prob-at-least-k 100100.05))
(display "P(10+ defaults | independent): ")
(display p-tail) (newline)
; With correlation, tail risk is MUCH higher; The Gaussian copula hid this fact
(display "Copula models assumed low correlation")
(display " -> underpriced senior tranches")
The CDS-bond basis is the difference between the CDS spread and the bond's credit spread over the risk-free rate. In theory the basis is zero (no-arbitrage). In practice, funding costs, liquidity premiums, and counterparty risk drive it away from zero. A negative basis (CDS cheaper than the bond spread) signals a potential arbitrage.