# 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.

• See your other question quant.stackexchange.com/questions/38114/…, the risky annuity is the LHS of your equation when you set $S_n$ to 1 – Antoine Conze Feb 11 '18 at 17:35