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.

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.

• Im not sure what Risky pv01 would be. Also whats at risk exactly – Permian Feb 10 '18 at 21:56
• Sorry this is what I really dont understand. What is the annuity paid by the reference entity? I literally have no clue as to what this is. – Permian Feb 11 '18 at 15:26
• What is not understood? An annuity is a level series of cash flows, for example 1bp for 10 years. The reference entity is the company whose default determines whether the CDS pays out. – dm63 Feb 11 '18 at 16:42
• Thats what i was missing – Permian Feb 11 '18 at 16:48
• 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