8.5 Credit Default Swaps (CDS): Mechanics, Pricing & Trading Strategies

8.5 Credit Default Swaps (CDS): Mechanics, Pricing & Trading Strategies

Core Insight: Credit Default Swaps (CDS) are the preeminent derivative instrument for transferring, pricing, and managing credit risk. At CFA Level II, candidates must master standardized CDS contract conventions, upfront premium mathematics, hazard rate default probabilities, and sophisticated relative-value trading strategies including basis trading and curve positioning.

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1. CDS Contract Mechanics & ISDA Conventions

The Basic CDS Structure

A Credit Default Swap (CDS) is a bilateral derivative contract transferring the credit exposure of a reference entity from the Protection Buyer to the Protection Seller.

                                  Periodic Fixed Coupon (e.g., 100 bps / 500 bps)
   +-----------------------+ -----------------------------------------------------> +-----------------------+
   |                       |                                                        |                       |
   |   Protection Buyer    |                                                        |   Protection Seller   |
   |      (Short Risk)     | <----------------------------------------------------- |      (Long Risk)      |
   +-----------------------+     Contingent Payoff upon Credit Event (100% - RR)    +-----------------------+

• Protection Buyer: Pays periodic coupon payments (the CDS spread) and receives a contingent payoff if a credit event occurs (economically equivalent to being short the credit risk / buying insurance).
• Protection Seller: Receives periodic coupon payments and agrees to make the buyer whole if a credit event occurs (economically equivalent to owning the underlying bond / long credit risk).
• Reference Entity vs. Reference Obligation: The reference entity is the legal corporate or sovereign issuer. The reference obligation is the specific debt instrument designated to establish seniority and deliverability (typically senior unsecured debt).

Defined ISDA Credit Events

Under International Swaps and Derivatives Association (ISDA) master agreements, a CDS payoff is triggered only by defined credit events:

1. Bankruptcy: The reference entity files for formal bankruptcy, insolvency, or liquidation.
2. Failure to Pay: The borrower fails to make contractual principal or interest payments after the expiration of a specified grace period (typically exceeding $1 million threshold).
3. Restructuring: Mandatory restructuring of debt terms (principal haircut, coupon reduction, or maturity extension) that harms bondholders. ISDA recognizes four restructuring conventions:
   • Complete Restructuring (CR): Any restructuring qualifies; deliverable bonds up to 30 years.
   • Modified Restructuring (MR - US Standard historically): Restructuring qualifies; deliverable debt capped at 30 months post-restructuring.
   • Modified Modified Restructuring (Mod-Mod R - European Standard): Deliverable debt capped at 60 months for restructured obligations and 30 months for other obligations.
   • No Restructuring (XR - Modern US IG Standard): Restructuring is excluded as a credit event entirely.

Settlement Mechanisms: Physical vs. Cash Auction

• Physical Settlement: The protection buyer delivers defaulted physical bonds of the reference entity to the seller in exchange for 100% par value in cash.
• Cash Settlement (Modern Market Standard): Established via an electronic Creditex / ISDA Credit Event Auction. Dealers submit two-way executable quotes to determine the post-default recovery price ($RR$). The protection seller pays the buyer: $\text{Contingent Cash Payoff} = \text{Notional Principal} \times (100\% - \text{Auction Recovery Rate})$

2. CDS Pricing, Valuation & Upfront Premium Mathematics

Post-Big Bang Standardized Coupons

Following the 2009 "Big Bang" and "Small Bang" regulatory reforms, all standardized CDS contracts trade with fixed, standardized annual coupons:

• Investment Grade (IG) Index & Single-Names: 100 bps (1.00%) per annum.
• High Yield (HY) Index & Single-Names: 500 bps (5.00%) per annum.

Upfront Premium Determination

Because an issuer's true market credit spread (the CDS Spread) rarely equals exactly 100 bps or 500 bps, counterparties exchange an Upfront Premium at trade inception to balance the present value of the Protection Leg and Premium Leg:

$\text{Upfront Premium} = \text{PV of Protection Leg} - \text{PV of Premium Leg}$

$\text{Upfront Premium (\$)} \approx (\text{CDS Spread} - \text{Fixed Coupon}) \times \text{Effective Spread Duration} \times \text{Notional}$

$\text{Upfront Premium (\% of Par)} \approx (\text{CDS Spread} - \text{Fixed Coupon}) \times \text{Effective Spread Duration}$

$\text{Price of CDS per 100 Par} = 100 - \text{Upfront Premium (\% of Par)}$

• If $\text{CDS Spread} > \text{Fixed Coupon}$: The contract is trading "above par." The protection buyer must pay an upfront cash premium to the seller (positive upfront).
• If $\text{CDS Spread} < \text{Fixed Coupon}$: The contract is trading "below par." The protection seller must pay an upfront cash premium to the buyer (negative upfront).

Hazard Rate and Survival Probability Formulation

Assuming a constant hazard rate (conditional default intensity $\lambda$):

$\text{Survival Probability to Year } t: \quad S_t = (1 - \lambda)^t \approx e^{-\lambda t}$ $\text{Unconditional Default Probability in Year } t: \quad PD_t = S_{t-1} \times \lambda = (1 - \lambda)^{t-1} \times \lambda$ $\text{Expected Loss in Year } t = S_{t-1} \times \lambda \times (1 - RR)$ $\text{Approximate CDS Spread} \approx \lambda \times (1 - RR) = \text{Hazard Rate} \times \text{LGD}$

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3. Worked Upfront Premium & Cash Settlement Numerical Model

Scenario 1: Initiating a 5-Year High-Yield CDS Contract

An asset manager purchases $10,000,000 notional of 5-year CDS protection on Titan Corp.

• Titan Corp Market CDS Spread: $680 \text{ bps}$ ($0.0680$)
• Standardized HY Fixed Coupon: $500 \text{ bps}$ ($0.0500$)
• Effective Spread Duration: $4.40 \text{ years}$

Step 1: Calculate Upfront Premium (% and $)

$\text{Upfront Premium (\%)} \approx (0.0680 - 0.0500) \times 4.40 = 0.0180 \times 4.40 = +0.0792 = \mathbf{+7.92\%}$ $\text{Upfront Cash Paid by Buyer} = \$10,000,000 \times 7.92\% = \mathbf{\$792,000}$

Step 2: Calculate Standard CDS Price

$\text{Price of CDS per 100 Par} = 100 - 7.92 = \mathbf{92.08}$

Scenario 2: Credit Event & Auction Cash Settlement

Two years later, Titan Corp defaults on its senior unsecured notes. An ISDA Creditex auction determines the final recovery rate to be $35.00%$ ($RR = 35%$).

• Loss Given Default: $LGD = 100% - 35% = 65.00%$
• Contingent Cash Payoff to Protection Buyer: $\text{Cash Settlement Payoff} = \$10,000,000 \times (100\% - 35\%) = \$10,000,000 \times 65.00\% = \mathbf{\$6,500,000}$

4. Advanced CDS Trading Strategies & Market Applications

Summary of Professional CDS Trading Strategies

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5. CDS-Cash Basis Trading Mechanics

The Basis Definition

The CDS-Cash Basis measures the pricing discrepancy between the derivative CDS spread and the cash bond Z-spread for the same issuer and maturity:

$\text{Basis} = \text{CDS Spread} - \text{Bond Z-Spread}$

Under No-Arbitrage: CDS Spread = Bond Z-Spread  (Basis = 0)
In Dislocated Markets:
- Negative Basis (CDS < Z-spread): Cash bond is underpriced relative to CDS. Strategy: Long Bond + Long CDS.
- Positive Basis (CDS > Z-spread): Cash bond is overpriced relative to CDS. Strategy: Short Bond + Short CDS.

Executing the Negative Basis Trade

1. Market Condition: A corporate bond trades at a Z-spread of $240 \text{ bps}$, while its 5-year CDS trades at $180 \text{ bps}$ ($\text{Basis} = 180 - 240 = -60 \text{ bps}$). The cash bond is cheap relative to CDS.
2. Portfolio Construction:
   • Buy the physical corporate bond yielding benchmark $+ 240 \text{ bps}$.
   • Buy 5-year CDS protection paying $180 \text{ bps}$.
3. Arbitrage Return / Positive Net Carry: $\text{Net Positive Carry} = 240 \text{ bps} - 180 \text{ bps} = +60 \text{ bps}$ The investor collects $60 \text{ bps}$ of net riskless spread while default risk is fully hedged by the CDS contract. As market liquidity normalizes and the basis converges to zero, the trade generates capital appreciation.