What is a credit default swap (CDS)?
A credit default swap is a contract — a type of financial derivative — that lets one party transfer the risk of a borrower failing to meet its debt obligations to another party. The buyer of protection pays the seller a periodic fee (or sometimes an upfront amount). In return, if a pre-defined “credit event” occurs for the referenced borrower (the “reference entity”), the seller compensates the buyer for the loss under the referenced debt instrument.
Key definitions
– Protection buyer: the party that pays premiums to obtain insurance against a credit event.
– Protection seller: the party that receives premiums and promises to compensate the buyer if a credit event occurs.
– Reference entity: the borrower or issuer whose credit risk is being insured (for example, a corporation, municipality, or sovereign).
– Notional amount: the face value of debt being insured (the size of protection).
– Running spread / premium: the periodic payment rate (often expressed in basis points; 100 basis points = 1%) paid on the notional.
– Credit event: a contract-specified trigger such as bankruptcy, failure to pay, restructuring, or repudiation that allows the buyer to claim payment.
– Physical settlement: the buyer delivers the defaulted bond to the seller and receives par value.
– Cash settlement: the seller pays the buyer the loss amount (par minus recovery value) instead of accepting the bond.
How a CDS works (step-by-step)
1. Two parties agree on the CDS terms: reference entity, notional, maturity, credit events, and settlement method. Standard contracts are often based on ISDA (International Swaps and Derivatives Association) documentation.
2. The protection buyer starts paying the agreed premium (running spread or, in some deals, an upfront payment plus a smaller running fee).
3. If no credit event occurs, the buyer continues paying until the contract expires; no further payments are made.
4. If a specified credit event occurs, the contract moves to settlement: either physical delivery of the defaulted bond for par, or cash payment equal to the loss amount. Cash settlement often uses an industry auction to determine recovery value.
5. After settlement, the CDS terminates.
When CDSs are used
– Hedging: A bondholder uses a CDS to reduce exposure to a borrower’s default risk.
– Speculation: Traders take positions in CDSs to profit from changing perceptions of creditworthiness without holding the underlying bond.
– Arbitrage: Investors can exploit price or spread differences between a bond and the matching CDS (for example, buying the bond and buying protection if the combined return is favorable).
Common credit events
Typical events that trigger settlement in single-name CDS contracts include bankruptcy, failure to pay scheduled amounts, and certain forms of restructuring or repudiation. The exact list is agreed in the contract.
Advantages and disadvantages (high level)
Pros:
– Provides a way to transfer credit risk without selling the underlying asset.
– Can improve risk management for lenders and portfolio managers.
– Traded instruments can be liquid and allow quick repositioning.
Cons and risks:
– Counterparty risk: if the protection seller cannot pay after a credit event, the buyer may not be fully protected.
– Market opacity: before reforms, many CDS trades were bilateral and opaque, increasing systemic risk.
– Complexity: variations in contract terms, settlement methods, and legal definitions can make outcomes uncertain.
– Speculation and leverage can magnify losses across the financial system (CDSs were implicated in the 2007–2009 financial crisis).
Practical checklist — what to review before entering a CDS
– Counterparty strength and credit support (margin/collateral arrangements
) – Contract details: reference entity (the borrower whose credit is being insured), reference obligation (which debt issue is covered), notional amount, maturity, currency, whether the contract is single‑name or an index, credit‑event definitions (default, failure to pay, restructuring), and any optionality or restructuring clauses.
– Settlement mechanics: physical settlement (protection seller delivers defaulted bond/loan) vs cash settlement (net cash payment). Know the ISDA determination procedure and typical auction process used to set the market recovery price after a credit event.
– Pricing and valuation assumptions: the contract spread (coupon) versus market (par) spread, assumed recovery rate, discount curve, and the implied default (hazard) rates. Check whether pricing is done using survival probability models or market‑implied spreads.
– Collateral and margin mechanics: frequency of margin calls, thresholds, minimum transfer amounts, eligible collateral, and rehypothecation rights. Consider what happens to collateral in the event of counterparty
default
– Legal and documentation review: confirm the ISDA Master Agreement, relevant Credit Support Annex (CSA), and the specific CDS confirmation. Key items to check:
– Governing law and forum for disputes.
– Who sits on the ISDA Determinations Committee for the reference entity and the rules for calling a credit event.
– Whether the CSA permits re-hypothecation and what collateral currencies and haircuts apply.
– Compression/novation provisions and whether the trade can be centrally cleared.
– Any tax gross-up or withholding clauses.
– Operational and infrastructure risks: verify back-office readiness and operational workflows.
– Trade capture fields: trade date, effective date, termination date, notional, spread (coupon), upfront payment (if any), and settlement method.
– Margin flows: frequency (daily/weekly), dispute resolution process, and operational cutoffs for collateral posting.
– Reporting and trade repository requirements (post-trade reporting jurisdiction depends on counterparty and reference entity).
– Reconciliation and breaks process between counterparties and custodians.
– Counterparty credit risk and replacement cost: estimate potential exposure and costs to replace protection.
– Calculate potential future exposure (PFE) for your position under stressed credit conditions.
– Include Credit Valuation Adjustment (CVA) in valuation to reflect counterparty default risk; for dealers, also include Debit Valuation Adjustment (DVA) if relevant.
Worked pricing and valuation — formulas and a simple numeric example
– Basic concepts:
– Spread (s): the ongoing periodic payment (usually quoted in basis points per annum) the protection buyer pays to the seller.
– Recovery rate (R): fraction of notional expected to be recovered if a default occurs.
– Hazard rate (λ(t)): instantaneous default intensity; survival probability S(0,t) = exp(-∫0^t λ(u) du).
– Discount factor P(0,t): present value factor to discount cash flows to today.
– Fair-par spread formula (continuous-time, general form):
s = (1 – R) * ∫0^T P(0,t) λ(t) S(0,t) dt / ∫0^T P(0,t) S(0,t) dt
– Numerator: present value of expected default loss (default intensity × loss given default).
– Denominator: present value of expected premium payments while alive (premium leg).
– Simple numeric example (constant hazard λ, constant discount rate r, maturity T):
– Assume: R = 40% (0.40), λ = 2% (0.02 per year), r = 1% (0.01), T = 5 years.
– Survival probability S(t) = exp(-λ t) = exp(-0.02 t).
– Discount P(0,t) = exp(-r t) = exp(-0.01 t).
– Evaluate integrals numerically (or use closed form when λ and r constant).
– PV of default leg ≈ (1 – R) * ∫0^T e^{-(r+λ)t} λ dt = (1 – R) * λ * (1 – e^{-(r+λ)T})/(r+λ)
– PV of premium leg ≈ ∫0^T e^{-(r+λ)t} dt = (1 – e^{-(r+λ)T})/(r+λ)
– Cancelling common factor (1 – e^{-(r+λ)T})/(r+λ) gives s ≈ (1 – R) * λ
– So s ≈ (1 – 0.40) * 0.02 = 0.012 = 120 bps × 0.1? Wait—check units: 0.012 = 120 bps? No: 0.012 = 120 basis points? Actually 1 bp = 0.0001 so 0.012 = 120 bps. But 0.012 corresponds to 120 bps. That is incorrect relative to typical numbers for λ=2%: (1-R)*λ = 0.6*0.02 = 0.012 = 120 bps. So the fair-par spread is 120 bps in this numeric example.
– Interpretation: with a 2% annual default intensity and 40% recovery, the par CDS spread ≈ 120 basis points.
Note: the simple result s ≈ (1-R)λ holds under constant λ and flat discounting. Real markets use a term structure of hazard rates and discount curves, accrual on default, and standard coupon conventions (typically 100 bps, 500 bps, or a floating coupon with upfront).
Practical checklist before entering a CDS trade
1. Confirm reference entity details (single-name CUSIP/ISIN, index version and series for indices).
2. Read the most recent ISDA definitions and any local jurisdiction addenda.
3. Validate recovery assumption on which pricing will be based.
4. Run valuation under multiple scenarios: base, stressed higher λ, lower recovery, and widening discount spreads.
5. Quantify counterparty exposure and determine collateral requirements and posting liquidity.
6. Check clearing availability: centrally cleared trades reduce bilateral counterparty risk but impose standardized terms.
7. Confirm tax and accounting treatment with your firm’s tax/accounting specialists (hedge accounting tests if used as a hedge).
8. Ensure operational readiness for settlement: auction mechanics, physical delivery logistics for bonds, or cash-settlement procedures.
How settlement typically works (practical example)
– Cash settlement via auction (common for indices and many single-name CDS):
– After an ISDA Determinations Committee declares a credit event, an auction sets a market recovery price R_auction.
– Protection seller pays: Notional × (1 – R_auction). The buyer keeps the defaulted bonds (if physical settlement) or receives cash (cash settlement).
– Example: Notional $10,000,000, R_auction = 20% → payout = $10,000,000 × (1 – 0.20) = $8,000,000.
– Physical settlement:
– Protection buyer delivers eligible bonds/loans (subject to eligibility matrix). The seller pays par for the delivered asset.
Common uses and strategies (educational)
– Economic hedging: protect bond exposure or portfolio credit
– credit protection for a corporate bond portfolio. Buy CDS protection sized to the bond face value to reduce loss if an issuer defaults. Match maturity and eligible obligations where practical; expect basis risk (see below).
– directional/speculative position. Traders short credit risk buy protection without holding the bond; traders long credit risk sell protection. Selling protection is like writing insurance and exposes you to potentially large losses if a credit event occurs.
– relative value and arbitrage. Use differences between cash bond spreads, CDS spreads, and funding/swap rates to capture a “basis” trade (see worked example).
– synthetic exposure and capital management. Financial institutions can create or hedge credit exposures synthetically (e.g., buying protection to reduce regulatory capital for a loan) or replicate a bond exposure using CDS and interest-rate instruments.
Key practical checks before using CDS (checklist)
1. Define objective: hedge, speculate, or arbitrage.
2. Choose notional and maturity to match exposure.
3. Confirm deliverable obligations and settlement method (physical vs cash).
4. Check current CDS spread and liquidity for the name/tenor.
5. Estimate recovery assumption — market typically uses auction recovery post-default; pre-trade you must pick a working assumption (e.g., 40%).
6. Assess counterparty terms: cleared vs bilateral, collateral thresholds, ISDA master agreement, upfront fees.
7. Calculate expected cost/benefit under scenarios (no-default, default at T, early default).
8. Monitor basis and mark-to-market daily; plan exits if needed.
Pricing intuition and simple formulas
A CDS is priced by equating the present value (PV) of two legs:
– Premium leg: periodic payments (spread s) paid until maturity or default.
– Protection leg: contingent payment (1 − R) × Notional paid if default occurs, where R = recovery rate.
In continuous-time, if h(t) is the hazard rate (instantaneous default intensity) and assuming constant h and constant discount factor for simplicity:
approximate fair spread s ≈ h × (1 − R).
Interpretation: spread compensates for expected loss per unit time (default probability × loss given default).
Discrete, simplified approximation (constant h, flat discount factor):
1. Annual default probability ≈ h (if small).
2. Expected annual loss ≈ h × (1 − R).
3. So s ≈ expected annual loss.
More formally, the equality is:
PV_premium_leg(s) = PV_protection_leg
where
PV_premium_leg(s) = s × Sum_{i} Δ_i × DF(t_i) × S(t_i),
PV_protection_leg = (1 − R) × Sum_{i} [DF(t_i) × (S(t_{i−1}) − S(t_i))],
DF = discount factor, Δ_i = accrual fraction, S(t) = survival probability to time t.
(This is the basis of standard CDS valuation models used by dealers.)
Worked numeric examples (rounded, no discounting unless stated)
Example A — Hedging a corporate bond
– Bond face: $5,000,000.
– Desired hedge: full notional, 5-year CDS.
– Market 5-yr CDS spread for issuer: 250 bps = 2.50% per year.
– Recovery assumption: 40% → loss given default (LGD) = 60%.
Annual premium cost (approximate, ignoring accrual and discounting):
= 2.50% × $5,000,000 = $125,000 per year.
Total premiums over 5 years (no discounting) = $625,000.
If default occurs at any time, protection payoff ≈ $5,000,000 × 0.60 = $3,000,000 (cash or par under physical delivery). The hedge cost is the stream of premiums; compare that to expected loss probability to evaluate value.
Example B — Simple CDS pricing via hazard rate
Assume constant hazard rate h = 3% per year, recovery R = 40%.
Approximate fair spread s ≈ h × (1 − R) = 0.03 × 0.60 = 0.018 = 180 bps.
Example C — Cash–CDS basis (arbitrage intuition)
Definition: cash–CDS basis ≈ bond spread (over a reference rate) − CDS spread.
If bond spread = 300 bps and CDS spread = 250 bps, basis = +50 bps (positive basis).
Arbitrage idea (informal): If basis is persistently positive, an investor could buy the bond and buy protection (locking in a “carry” roughly equal to basis minus financing/counterparty costs). Profit requires funding and collateral costs, and execution risk; careful modeling and collateralization matter.
Primary risks of using CDS (with mitigation ideas)
– Counterparty risk: the party selling protection may default. Mitigate with central clearing, collateral arrangements, or trade with well-rated counterparties.
– Basis risk: CDS may not perfectly offset bond losses due to differences in eligible deliverables, restructurings, or index vs single-name specifics. Mitigate by matching definitions and maturities.
– Liquidity risk: Wide bid–ask spreads, especially in stressed markets. Use liquid names/tenors where possible.
– Legal and documentation risk: ISDA terms, credit event definitions, and auction mechanics matter. Review agreements and eligibility matrices.
– Jump-to-default risk and mark-to-market volatility: sudden large moves can require immediate collateral posting. Stress-test liquidity and collateral buffers.
– Model risk: valuation depends on recovery assumptions, hazard
…rate, recovery assumptions, and discount factors; mitigate with sensitivity analysis, scenario testing, and use of multiple valuation approaches (e.g., reduced‑form vs structural models).
Valuation basics — what you equate
– Protection leg: the expected present value (PV) of the payment that the protection seller makes if default occurs (usually (1 − R) times notional, where R is the recovery rate).
– Premium (or fee) leg: the PV of the periodic payments the protection buyer makes (the running spread s or an upfront payment plus a smaller running spread).
Fair value (par) condition: PV(protection leg) = PV(premium leg). Solve for the spread s (or the upfront) that makes the equality hold.
Continuous-time, flat-rate intuition (useful closed form)
Assume constant hazard rate λ (instantaneous default probability), constant recovery R, and constant risk-free rate r. With continuous compounding:
– Survival probability to time t: S(t) = e^(−λt).
– PV of protection leg (continuous default arrivals): PV_prot = ∫0^T (1 − R) λ e^(−(r+λ)t) dt = (1 − R) λ/(r + λ) [1 − e^(−(r+λ)T)].
– PV of premium leg (continuous payment stream at rate s): PV_prem = s ∫0^T e^(−(r+λ)t) dt = s/(r + λ) [1 − e^(−(r+λ)T)].
Cancel common factor [1 − e^(−(r+λ)T)]/(r + λ) and you get the simple relation:
s ≈ (1