A credit default swap premium is the compensation a protection buyer pays the protection seller for credit protection under a credit default swap (CDS). The running part is quoted as an annual rate on the contract's notional, but the cash payment depends on the accrual period. A trade may also require an upfront payment. Confusing the annual rate with a period payment, or a fixed coupon with the market par spread, misstates the cost of the hedge.
Reading the coupon in cash
Consider a wholly fictional CDS with USD 10 million notional and a running coupon of 100 basis points per year. Stipulate a complete accrual period of 90/360 years, with no covered credit event during that period. These are example conventions, not a claim that every CDS quarter contains 90 days.
For notional , annual coupon rate and contractual accrual fraction , the scheduled premium is
Here bp is per year, so the buyer pays the seller
The notional scales the payment; it is not principal advanced to the seller as part of this coupon. USD 100,000 is the annualized coupon amount on this notional. USD 25,000 is the cash for the stipulated period. Neither amount is the price of all remaining protection.
Original synthetic ledger. The top panel calculates one full-period coupon. The lower panel separates running-premium present value from value-balancing upfront; its risky annuity is a valuation input, not a promised payment horizon.
Coupon, par spread and upfront answer different questions
The fixed running coupon determines the contractual periodic rate. The par CDS spread is the annual rate that would balance the modeled protection and premium legs without a value-balancing upfront payment, on a consistent accrual basis. The upfront bridges the value difference when the actual coupon differs from that par rate. ISDA's standard-model overview explains why fixed coupons and upfront payments require a standardized conversion to spread quotations.
To see the accounting, let be the risky premium annuity: the discounted, pricing-measure expected accrual time per unit notional. It includes survival-contingent scheduled premiums and any default-accrual payment required by the assumed contract. Write for the protection leg's present value. Ignoring counterparty failure and fees, the running-premium leg has value . At a fresh valuation point with no initial accrued-premium adjustment,
where positive means the buyer pays the seller upfront. Keep all present values at the same valuation date and in the same currency.
For a separate synthetic valuation, stipulate years, bp per year and the same USD 10 million notional and 100 bp coupon. The running-premium PV is USD 400,000; the protection PV is USD 600,000. The buyer therefore pays USD 200,000 upfront. The coupon remains 100 bp. Subtracting 100 bp from 150 bp gives a rate difference; multiplying by notional and the risky annuity converts it into money.
An executed trade's settlement amount can also include an accrued-premium adjustment. Separate that from the value-balancing upfront when reconciling a quote. The New York Fed's discussion of a CDS-bond trade provides a practical setting in which periodic premiums and an upfront both matter.
Why the full schedule matters
A covered event can change the premium cash flows. The Chicago Fed's CDS pricing appendix includes both survival-contingent scheduled premiums and premium accrued through a default date. For an actual trade, use its documented day count, accrual boundaries, payment adjustments and credit-event terms. The simple 90/360 calculation above applies only to the stated full-period scenario.
A higher par spread does not automatically reset an existing fixed coupon. It changes the value of the remaining protection relative to the contracted payments. Nor is a spread itself a physical probability of default: pricing also depends on recovery, discounting, timing and compensation for bearing risk.
For the next mathematical step, Reduced-Form Models: Hazard Rates and Risk-Neutral Default Probabilities derives survival-weighted premium and protection legs in a simplified hazard model. Its displayed CDS formula omits accrued premium at default; it is a pricing foundation rather than a complete contractual settlement calculation. The public page is a preview; the full lesson requires membership.
Sources
- ISDA CDS Standard Model, background on fixed coupons, upfront payments and spread conversion.
- Federal Reserve Bank of Chicago: What Does the CDS Market Imply for a U.S. Default?, October 2023, appendix equations A1–A6 and appendix note i.
- Federal Reserve Bank of New York: Credit Market Arbitrage and Regulatory Leverage, January 2017, “The Mechanics of the Spread Trade.”
- Alexander J. McNeil, Rüdiger Frey and Paul Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, revised edition, Princeton University Press, 2015, §10.1.4, pp. 370–371, and §10.4.4, pp. 402–403. The latter explicitly simplifies away accrued premium at default.