Foundational Intuition
A Credit Default Swap (CDS) is a derivative that separates credit risk from a loan or bond. It involves two parties: the Protection Buyer (who pays a spread) and the Protection Seller (who assumes the risk).
The Bilateral Payout Mechanism
How CDS Works Step-by-Step
- 1Setup:
Bank A owns $10M of Tesla bonds but wants to hedge credit risk without selling the bonds.
- 2Contract:
Bank A buys CDS protection from Hedge Fund B, paying 150bps annually on $10M notional.
- 3Payout:
If Tesla defaults, Hedge Fund B pays Bank A the loss: $10M × (1 - Recovery Rate).
Reference Entity
The corporation or sovereign whose credit is being tracked. Note the Entity is the name, while the Obligation is the specific bond used to determine seniority.
Insurable Interest
Unlike insurance, CDS do not require the buyer to suffer a "loss." This allows for Long/Short Credit strategies.
ISDA Credit Events
These are the specific triggers that activate CDS payouts. Understanding each is crucial for risk assessment:
Pricing and Valuation
CDS valuation relies on modeling Hazard Rates (λ), the instantaneous probability of default given survival. This allows us to construct the Survival Probability curve P(t).
Survival Probability
The Premium Leg
The PV of periodic spread payments, conditional on survival. The protection buyer pays this.
The Protection Leg
The PV of the contingent payout (1-R) upon default. The protection seller pays this.
The Credit Triangle Simplification
For "napkin math," traders use the Credit Triangle relationship. For a flat curve and low default probability, the fair spread (s) simplifies to:
The Credit Triangle
The Big Bang Protocol
Before 2009, CDS traded with "Par Spreads" (coupons that made NPV=0). Post-Big Bang, coupons are fixed at 100bps or 500bps to facilitate Trade Compression and Central Clearing.
Pre-2009: Bespoke Contracts
Each contract had unique par spreads, no standardization, high bilateral risk, and was illiquid.
Post-2009: Standardized World
Fixed coupons (100bps or 500bps), standard terms (IMM dates), central clearing (ICE Clear Credit), and highly liquid.
Points Upfront (PUF) Calculation
Points Upfront Formula
Credit Event Auctions
To handle massive volumes of CDS during a default, ISDA introduced the Auction mechanism. Market participants submit bond bids to find a "Final Price." The CDS payout is simply (100 - Final Price), avoiding the physical delivery of scarce bonds.
Risk Sensitivities (CS01)
CS01 (Credit Spread 01) is the dollar change in NPV for a 1bp shift in the credit spread. It is fundamentally linked to Risky Duration (RD), which is the sensitivity of the Premium Leg to the spread.
CS01 Calculation
Credit Convexity (Negative Gamma)
CDS are non-linear. Credit Gamma measures the change in CS01 as spreads move. For a protection seller, the contract displays Negative Gamma. As spreads widen, your losses accelerate, but as they approach infinity, the loss per basis point (CS01) actually shrinks as the payout becomes certain.
For Protection Sellers
Losses accelerate in initial spread widening. Need larger hedges than CS01 suggests. Consider gamma hedging.
For Protection Buyers
Benefit from negative gamma of sellers. Gains accelerate in spread widening. Natural hedge for credit portfolios.
Precise Estimation
Calculating CS01 without a pricing engine requires estimating the Risky Duration (RD). This is essential for quick risk assessments and trade sizing.
Manual CS01 Estimate
Stress Testing Logic
Professional desks use three tiers of stress testing to ensure they can survive a systemic or idiosyncratic credit crash.
Tier 1: Linear Stress
A "Systemic Widening" shock (e.g., +200bps). 1st order estimate used for daily risk reporting. Loss = CS01 × Δs.
Tier 2: Jump-to-Default
Assumes an instantaneous credit event. Removes all probability modeling and calculates the actual cash payout: JTD = N(1 - R) - MTM.
Tier 3: Recovery Shock
In a crisis, Wrong-Way Risk occurs: spreads widen and Recovery rates drop simultaneously. Captures systemic credit cycles.