Credit Default Swaps: Pricing the Insurance

The defaults above (100 bps, 40% recovery, 5-year horizon) recreate the textbook senior-unsecured worked example. Annualized PD approximately equals 100 / (10000 x 0.60) = 1.67%/year. Compounded over 5 years using the survival-probability approach (1 minus (1 - 0.0167)^5) gives a cumulative PD approximately 8.05% over the life of the swap. The seller is being paid 100 bps per year, or roughly 500 bps total over the contract life (ignoring funding, discounting, and counterparty risk), in exchange for a payout of (1 - 0.40) x notional = 60% of notional if a credit event hits. The expected loss for the seller: 8.05% x 60% = 4.83% of notional, very close to the 5.00% gross premium collected. The small residual is the seller's compensation for funding cost, capital charge, and the convexity of the survival curve. Drag the par spread to 500 bps (high-yield territory) and the implied annualized PD jumps to about 8.33% — well into junk-rated default rates. This formula is the right first-cut intuition; real dealer pricing uses a survival-probability curve calibrated across multiple CDS maturities, not a single flat approximation.

CDS quotes are the highest-frequency, real-time pricing signal of credit risk that exists in the markets — typically updating faster than rating-agency action and often anticipating bond-spread moves. But a CDS quote is also a contract with frictions: counterparty risk, funding cost, recovery uncertainty, and the political/legal definition of what counts as a 'credit event' (the restructuring debate is real). Read a CDS spread as a market-consensus probability of default WEIGHTED by an assumed loss given default — and remember the assumption matters. A flat 40% recovery assumption misprices a senior-secured bond (typically 70-90% recovery) and a deeply subordinated bond (typically 10-25%); CDS dealers use product-specific recoveries even when they quote flat headline spreads.

Going Deeper — three frictions that distort the textbook CDS pricing equation. The clean par-spread approximation (spread approximately equals PD x LGD) is exactly right in a stylized model and approximately right in calm markets. Three frictions distort it in practice. (1) Recovery-rate uncertainty: dealers quote off a flat 40% senior-unsec assumption, but actual recoveries vary widely by company, jurisdiction, and economic regime. The 2009 GM bankruptcy settled at a recovery of about 12.5% — well below the 40% standard — meaning protection buyers on the standard assumption were UNDER-hedged on actual LGD. (2) Counterparty risk on the seller: the protection is only as good as the protection seller's ability to pay on a credit event. Pre-2008, AIG had written tens of billions in protection without posting commensurate collateral; when its own credit deteriorated, the value of AIG-written CDS fell sharply EVEN THOUGH the reference entities had not defaulted. Post-2009 standardization (mandatory clearing for most index CDS, daily margining) closed most of this gap but not all. (3) Restructuring vs no-restructuring contracts: the contract type matters. North American post-2009 standard contracts exclude restructuring as a credit event (XR clause); European contracts typically include modified restructuring (MR). The same name will trade at meaningfully different spreads under XR vs MR because the set of triggering events is different. Reading a CDS quote means reading the underlying contract, not just the headline number. AI prompt: 'For this ticker's CDS market, walk through the par-spread approximation, the assumed recovery rate, and the current CDS-bond basis. What does each tell me about the market's view of default risk that the bond spread alone does not capture?'