CDS

Part 6 gave survival probabilities from a hazard rate, recovery of par, and the present value of a payment that depends on default. A credit default swap exchanges payments that depend on the same default time, so each of its legs is a discounted expectation over the default intervals. The credit-curve chapter also uses the discount curve of Part 3.

This part values a credit default swap in a toy model and connects the value to the way the market quotes it. The first chapter builds the premium and protection legs from exact default-time expectations and solves the par spread. The second chapter converts a market-standard quote into a signed upfront amount against a fixed running coupon, and back. The third chapter separates what the market shows from what the model assumes or solves, and fits a credit curve to several tenors. The last chapter measures a position’s sensitivity to the liquid contract’s quote and sizes the equivalent notional that offsets it.

Part 7 of 74 chapters21 numbered equations4 knowledge checks

CDS premium and protection legs
Build exact default-time expectations for the two CDS legs and solve the zero-upfront par spread.
2 equations1 checkdraft
CDS market-standard quote and upfront
Distinguish a conventional CDS spread quote from a fixed running coupon, identify which quantity is observed and which is solved, calculate the signed upfront amount, and reverse the simplified conversion.
8 equations1 checkdraft
Credit curve and market observables
Separate what the CDS market shows from what a pricing model assumes or solves, read a credit curve as tenor marks plus a fitted survival curve, and distinguish transforming quotes from fitting the curve.
4 equations1 checkdraft
Equivalent notional and quote risk
Measure a CDS position's sensitivity to the liquid tenor's quote by bump and reprice, then size the liquid-tenor equivalent notional and equivalent ratio that offset it.
7 equations1 checkdraft

The argument

Each leg is a discounted expectation over the default intervals
The par spread makes the two legs equal with zero upfront
A market quote converts to an upfront amount against a fixed coupon
Several tenor marks fit a piecewise-constant hazard curve
Bump and reprice gives the quote risk, and the equivalent notional offsets it

After this part you can

Interpret a CDS as running-premium payments exchanged for contingent protection, partition default into disjoint time events, and read the protection buyer's signed value as protection minus premium.
Calculate the positive premium-leg present-value magnitude from scheduled survival-contingent premiums and exact accrued premium integrated over modeled default time under the stated constant-hazard model.
Calculate the positive protection-leg present-value magnitude by integrating discounted loss-given-default over exact modeled default time under the stated constant risk-neutral hazard.
Calculate the zero-upfront CDS running spread that equates the exact default-time premium- and protection-leg present-value magnitudes under one internally consistent model.
Distinguish the lesson's market-standard quote from the fixed running coupon and explain the quote's role in a simplified CDS conversion.
Calculate the signed upfront amount that makes protection-buyer inception value zero for an input quote-implied premium annuity and fixed running coupon.
Calculate the market-standard quote implied by a signed upfront amount under the lesson's simplified flat-hazard conversion.
Classify each quantity in a standard CDS valuation as market-observed, contractual, conventional, or model-solved, and explain why the traded upfront alone identifies the pricing-model hazard rate.
Interpret a credit curve as the term structure of standard-contract marks at quoted tenors together with the survival curve fitted to them, and distinguish a tenor-by-tenor change of quotation from a fit of one hazard term structure.
Calculate the survival probability implied by fitted piecewise-constant hazard segments and verify that a tenor's standard contract reprices to its mark under the fitted curve.
Calculate a CDS position's signed value change for a one-basis-point rise in the liquid tenor's market-standard quote by re-solving the flat hazard rate and revaluing the position for its own side.
Calculate the notional and side of the most liquid standard CDS that offsets a position's sensitivity to the liquid tenor's quote, and express it as an equivalent ratio to the position notional.