howard-lynn-ye CDS mechanics and upfront
A single-name CDS trades on a fixed coupon with an upfront payment, so the quoted "spread" is
a quoting device, not a cash flow. Two steps convert one to the other and both have a trap in
them: upfront = (quoted spread − coupon) × RPV01, where RPV01 is the risky annuity in years,
not the tenor — and the tenor is not the tenor either, because "5Y" is a 20 June or
20 December date somewhere between 4.75 and 5.25 years away.
Measured figures below are printed by scripts/cds.py (runs in 1.0 s; scipy plus pure
python dates, QuantLib optional). ✅ Measured means this file produced it on 2026-09-09 with
QuantLib 1.43, scipy 1.13.0, Python 3.11.3. Conventions are ✅ source-verified against ISDA's own
documents at cdsmodel.com, read 2026-09-09.
The rule:
upfront = (quoted spread − coupon) × RPV01, and RPV01 is the risky annuity. Never multiply by the tenor, and never trust the label — read the maturity date.
1. ✅ ISDA's own worked example, reproduced exactly
✅ Source: ISDA, Standard CDS Examples (April 2009) and Standard North American Corporate
CDS Contract Specification (version 4 March 2009), both published at cdsmodel.com. A 1-year
$36mm 100 bp standard CDS traded in Feb-09 maturing 20 Mar 10. ✅ isda_worked_example()
rebuilds the schedule from the conventions and matches every published figure:
| # | accrual start | accrual end | days (ISDA) | payment (ISDA) | payment date |
|---|---|---|---|---|---|
| 1 | 2008-12-22 | 2009-03-20 | 88 (88) | $88,000 ($88,000) | 2009-03-20 |
| 2 | 2009-03-20 | 2009-06-22 | 94 (94) | $94,000 ($94,000) | 2009-06-22 |
| 3 | 2009-06-22 | 2009-09-21 | 91 (91) | $91,000 ($91,000) | 2009-09-21 |
| 4 | 2009-09-21 | 2009-12-21 | 91 (91) | $91,000 ($91,000) | 2009-12-21 |
| 5 | 2009-12-21 | 2010-03-20 | 90 (90) | $90,000 ($90,000) | 2010-03-22 |
✅ And the cash, quoted at 2 points upfront: buyer pays clean $720,000, seller pays $61,000 of accrued over 61 riskless days, net the buyer pays $659,000 — ISDA's published $720k / $61k / $659k to the dollar.
Three conventions do all the work in that table, and each is a way to be a day out:
- ✅ "Maturity Date: A CDS Date, unadjusted" — row 5 accrues to Saturday 20 Mar 10 and pays on Monday 22 Mar 10. Accrual dates are adjusted Following; the last one is not.
- ✅ The last accrual period includes the maturity date, so its 90 days is one more than the difference of its endpoints. Every other period is end-exclusive.
- ✅ "Accrual Begin Date: latest Adjusted CDS Date on or before T+1 calendar" — the adjusted date. On 9 Sep 2026 that is 22 Jun 2026, not 20 Jun, and the two differ by 2 days of accrued.
2. 🚨 The trap: RPV01 is the risky annuity, not the tenor
✅ Measured on a standard contract traded 2026-09-09, quoted 200 bp against a 100 bp coupon, R = 40%, flat 3% curve:
| ✅ value | |
|---|---|
| standard 5Y maturity | 2031-06-20 (accrual begins 2026-06-22) |
| protection actually bought | 4.7808 years, not 5.0000 |
| implied flat hazard (the quoting convention) | 3.546655% |
| risky annuity RPV01 | 4.367676 years |
clean upfront (S − C) × RPV01 |
4.367676 points |
| less accrued coupon (80 riskless days) | 0.222222 points |
| = cash settlement amount, paid by the buyer | 4.145454 points |
🚨 (S − C) × tenor |
5.000000 points — +14.48% |
🚨 $144,800 too much on $10mm, from an arithmetic shortcut that looks like it cannot be wrong.
✅ Where the years go
The label and the multiplier are separated by four independent steps, ✅ each measured:
| step | years |
|---|---|
| the label says | 5.0000 |
| calendar life of the standard contract | 4.7808 |
| ACT/360 accrual on the real IMM schedule | 5.0694 |
| after discounting at 3% | 4.7205 |
| after survival at the implied hazard | 4.3493 |
| plus accrual on default | 0.0184 |
| = RPV01 | 4.3677 |
Discounting and survival are the two that matter, and survival is the bigger one. The ACT/360 accrual is longer than five calendar years (5.0694), which is why "it is about five, so multiply by five" survives a sanity check.
🚨 The error grows with the tenor and with the spread
Both directions are the same mechanism — more years, or a lower survival probability, means a larger gap between the annuity and the tenor. ✅ Measured:
| tenor | maturity | RPV01 | vs tenor | 🚨 error of (S−C) × tenor |
|---|---|---|---|---|
| 1Y | 2027-06-20 | 0.9857 | −1.43% | +1.45% |
| 3Y | 2029-06-20 | 2.7857 | −7.14% | +7.69% |
| 5Y | 2031-06-20 | 4.3677 | −12.65% | +14.48% |
| 7Y | 2033-06-20 | 5.7618 | −17.69% | +21.49% |
| 10Y | 2036-06-20 | 7.5447 | −24.55% | +32.54% |
| quoted spread | implied flat hazard | RPV01 | 🚨 error |
|---|---|---|---|
| 50 bp | 0.8841% | 4.6288 | +8.02% |
| 100 bp (= the coupon) | 1.7698% | 4.5395 | n/a — upfront is zero |
| 200 bp | 3.5467% | 4.3677 | +14.48% |
| 500 bp | 8.9220% | 3.9016 | +28.15% |
| 1000 bp | 18.0504% | 3.2642 | +53.17% |
🚨 On a distressed name the shortcut is 53% wrong — exactly where the upfront is largest and the trade is most likely to be done in a hurry. ✅ The single point where it is right is the one place there is nothing to compute: when the quote equals the coupon and the upfront is zero.
3. 🚨 "Five year" is not five years
✅ Source-verified: ISDA specifies "CDS Dates: 20th of Mar/Jun/Sep/Dec" and "Maturity
Date: A CDS Date, unadjusted". ✅ Under the post-2015 convention — verified against QuantLib
1.43's own cdsMaturity(..., DateGeneration.CDS2015) on 4,000 (trade date, tenor) pairs with
0 mismatches — contracts mature on 20 June or 20 December and roll on 20 March and
20 September.
✅ Measured across the September 2026 roll:
| trade date | standard 5Y maturity | protection years |
|---|---|---|
| 2026-09-14 | 2031-06-20 | 4.7671 |
| 2026-09-18 | 2031-06-20 | 4.7562 |
| 2026-09-21 | 2031-12-20 | 5.2493 |
| 2026-09-28 | 2031-12-20 | 5.2301 |
🚨 The same "5Y" quote steps from 4.7562 to 5.2493 years over one weekend, and over a full cycle it ranges 4.7534 to 5.2548 — a spread of 0.5014 years. A "5Y CDS" position marked against a "5Y CDS" quote from before the roll is marked against a different contract. Store the maturity date, not the tenor label, and compare quotes only within a trading period.
⚠️ The 2009 ISDA specification above predates the 2015 change; it describes quarterly rolls with maturities on any CDS date. The 20 Jun / 20 Dec + semiannual-roll rule is verified here against QuantLib's implementation, not against an ISDA document.
4. ✅ The flat hazard is a quoting convention, not a model
✅ Source, verbatim, ISDA Standard CDS Examples: the converter "assumes a single flat hazard rate rather than a term structure of flat spreads", "credit risk begins at the end of the trade date (T)", and "Points upfront (and clean price) include only the value of risky days" — the days from the accrual begin date through T are riskless and contribute only to the coupon.
That is the whole reason the accrual rebate exists. The buyer will pay a full quarterly coupon covering days they did not own protection for, so at settlement the seller hands back the accrued: ✅ 80 riskless days = 0.222222 points on the 2026 contract in §2, taking the payment from 4.367676 clean to 4.145454 cash. 🚨 Comparing a clean upfront with a cash settlement amount is a real 22 bp of notional, and both are called "the upfront".
🚨 Do not read the flat hazard as a credit view. It is one number chosen to reproduce one
quote; it has no term structure and it is not the hazard you would estimate. Everything about
hazard-rate models, recovery sensitivity, and risk-neutral versus physical default probability
belongs to ../../../fin-models/skills/credit-risk-models/SKILL.md and is deliberately not
repeated here.
⚠️ Two more conventions worth knowing and not verified beyond the 2009 documents: the 40% standard recovery used in the conversion is a market convention, not a measurement; and cash settles T+3 (ISDA's example settles a 20 Feb 09 trade on 25 Feb 09).
✅ And a genuinely surprising one, quoted from the contract specification: "Legal Protection Effective Date: today −60 days for credit events and today −90 days for succession events". Protection is retroactive by 60 days. The T+1 start used in pricing is a valuation convention for events not yet known, not the contract's coverage.
5. ✅ The coupon is packaging; the upfront absorbs it
✅ Measured, same 200 bp name on each standard coupon:
| coupon | RPV01 | clean upfront | PV of protection |
|---|---|---|---|
| 100 bp | 4.3677 | +4.3677 points | 0.08735352 |
| 500 bp | 4.3677 | −13.1030 points | 0.08735352 |
✅ Identical PV to eight decimals. The upfront is exactly the PV of the difference between the quoted spread and whichever coupon was chosen, which is what makes 100 bp and 500 bp quotes comparable at all — and why a sign flip on the upfront is a 17.5-point error, not a typo.
6. 🔴 The ISDA Standard Rate Curve moved
✅ Read at cdsmodel.com on 2026-09-09: the ISDA Standard Rate Curves are now published at https://rfr.spglobal.com/. 🔴 The old https://rfr.ihsmarkit.com/ was decommissioned on 2026-08-15. Any pipeline or notebook that hard-codes the IHS Markit host is dead, and the failure is a network error at curve-build time, not a wrong number. The model itself is open source and maintained by S&P Global as administrator.
7. ✅ Cross-check against QuantLib 1.43
Same contract, three engines:
| fair spread | RPV01 | upfront | |
|---|---|---|---|
MidPointCdsEngine |
200.0924 bp | 4.365713 | 4.3697 pts |
IntegralCdsEngine |
200.0702 bp | 4.365965 | 4.3690 pts |
IsdaCdsEngine |
200.0598 bp | 4.366370 | 4.3690 pts |
| this file | 200.0000 bp | 4.367676 | 4.3677 pts |
✅ Worst disagreement 0.0924 bp of spread and 0.001962 years of RPV01. ⚠️ Note the three engines differ from each other by 0.0326 bp on identical inputs — they discretise the default time differently. If you are reconciling to a counterparty, the engine is part of the trade description.
🚨 ql.Settings.instance().evaluationDate is a global; a stale one gives NPV exactly 0.0.
Every QuantLib call above sets it before building a curve.
8. What the script gives you
scripts/cds.py — scipy (brentq) and datetime only; QuantLib imported inside two functions.
| Function | Does |
|---|---|
isda_contract_spec() / isda_converter_assumptions() |
§1, §4, the quoted conventions with their source |
isda_worked_example() |
§1, ISDA's published table and cash, reproduced |
following(d) / previous_imm / next_imm / previous_roll |
the CDS calendar |
standard_cds_maturity(trade_date, tenor) |
§3, the CDS2015 rule |
accrual_begin(trade_date) / accrued_days |
§1, the adjusted-date subtlety |
cds_periods(trade_date, maturity) |
the schedule as Period records |
premium_leg / protection_leg / par_spread |
closed-form legs, accrual on default included |
implied_flat_hazard(quoted_spread, ...) |
§4, the converter convention |
upfront(quoted_spread, coupon, ...) |
§2, clean, accrued and cash, plus the naive error |
rpv01_decomposition() |
§2, where the years go |
annuity_trap(tenors) / spread_sensitivity(spreads_bp) |
§2, both directions of the trap |
roll_jump() / roll_cycle_range() |
§3 |
coupon_invariance() |
§5 |
quantlib_roll_check() / quantlib_cross_check() |
§3, §7, or None |
Where this sits
../../../fin-models/skills/credit-risk-models/SKILL.md— the hazard rate as a model: Merton,N(−d2), constant hazard,lambda(1−R), recovery sensitivity, and the risk-neutral versus physical gap. This skill only uses a flat hazard as a quoting device and defers all of that.../credit-spread-measures/SKILL.md— the other credit spread. A CDS par spread and a bond Z-spread are different instruments; the basis between them is a trade, not an error.../corporate-bond-data-and-trace/SKILL.md— the cash-bond leg of that basis, and why a 15-minute-old bond print shows up as basis that is not there.../ratings-transitions-and-migration/SKILL.md— the 100 bp / 500 bp coupon split follows the investment-grade / high-yield line, so it moves when the rating does.../../../fin-models/skills/term-structure-models/SKILL.md— the discount curve every leg above is priced on. 🚨 A zero rate is a triple (day count, compounding, instrument); the ISDA Standard Rate Curve is a specific one, published daily at the site in §6.../../../fin-libraries/skills/lib-quantlib/SKILL.md—cdsMaturity,DateGeneration.CDS2015,FlatHazardRate, the three CDS engines, and 🚨 theevaluationDateglobal.../../../fin-core/skills/market-data-sourcing/SKILL.md— ⚠️ single-name CDS quotes and index composition are licensed (S&P Global / Markit); there is no free constituent feed. The ISDA Standard Rate Curve in §6 is free; the credit quotes are not.