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How Risky Annuity Converts CDS Spread Changes into Value

Article Quant Q&A · Author: Trajan
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Summary

The document explains why a credit default swap’s mark-to-market value depends on risky annuity, also called risky PV01. A change in the CDS spread is quoted in basis points per year, so the spread difference alone does not express the position’s value in currency. Multiplying that difference by the present value of the contract’s premium payments converts the annual spread change into a monetary amount for the notional.

The example considers selling protection at a higher spread and later seeing the market spread fall. The resulting spread advantage represents a stream of premium savings, whose value is scaled by the risky annuity. The annuity is “risky” because premium payments stop if the reference entity defaults. This is an intuitive first-order explanation; the document does not develop curve construction, discounting conventions, accrued premium, or the full valuation of contingent protection payments.

Key ideas

  • A CDS spread change is an annualized rate difference, not a currency value by itself.
  • Risky PV01 converts a basis-point spread difference into value by scaling it by the premium-leg annuity.
  • The annuity is risky because payments cease if the reference entity defaults.
  • The explanation gives an intuition for mark-to-market and omits detailed valuation conventions.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Mark to Market of a CDS Contract and Risky Annuities


# Mark to Market of a CDS Contract and Risky Annuities












From JP Morgan's Trading Credit Curves 1 and we have that:

> The MTM of a CDS contract is (for a sell of protection) therefore: $$\text{MTM} = (S_{\text{Initial}}-S_{\text{Current}}).\text{Risky Annuity}_{Current}.Notional$$

Why do we need the Risky Annuity Current? I dont see the logic behind this...

> Apparently the Risky Annuity is the present value of a 1bp annuity given a spread curve.

What is the point of this quantity? I literally cannot see why it appears anywhere.

> The first order effect that we need to consider is that of spread movements captured by our (Risky) Duration/ Risky Annuity

I am somewhat familar with fixed income duration and cannot see why we are considering the quantity (Risky) Duration/ Risky Annuity.

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/38176

ok so if you sell a CDS for 100bp and then the market moves to 90bp, you have a profit of 10bp. But how much is that actually worth in dollar terms? Suppose you then buy the CDS for 90bp, what have you got? You have 10bp per annum until the reference entity defaults, which is worth 10bp * the Risky pv01 of the contract. Hope that explains it.

The risky pv01 is the value of a 1bp annuity paid by the reference entity. It is 'risky' because if the reference entity defaults, it stops.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.