# From quoted spread and coupon to upfront, and vice versa : which recovery rates and when?

Echoing the following question :

Markit recovery rates : assumed vs real

I would like to have a confirmation on my understanding on the matter.

Markit provides data for CDS, namely, for tenors blonging to (6M, 1Y,...,10Y, 15Y, 20Y and 30Y) Markit provides corresponding "quoted spreads" (that they call conventional spreads) and corresponding upfronts (the clean price of the protection leg minus the clean price of the premium leg). Markit provides also two recovery rates : the assumed recovery rate and the real recovery rate.

What I understand is that, to go back and forth between quoted spread and upfront, for a given tenor, one proceeds as follows :

1. Given a quoted spread and a coupon, one finds the flat default intensity $\lambda_0$ such that the par spread (in the ISDA model) calculated with the coupon, $\lambda_0$ and the assumed recovery rate is equal to the quoted spread, and using this $\lambda_0$, the upfront is the price (in the ISDA model with constant default intensity $\lambda_0$) of the CDS with the given coupon and the real recovery rate.
2. Given an upfront and a coupon, one finds the flat default intensity $\lambda_0$ such that the price (in the ISDA model with constant default intensity $\lambda_0$) of the CDS with the given coupon and the real recovery rate is equal to the upfront, and then the quoted spread is the par spread (in the ISDA model) calculated with the coupon, $\lambda_0$ and the assumed recovery rate.

Am I wrong, and is only the assumed recovery rate used ?

• the real recovery rate $R_{\textrm{real}}$ is used for pricing a cds outside of a conversion context : it is $\textrm{Notional}\times (1 - R_{\textrm{real}})$ that is payed is case of default.
For a non distressed name, assumed and real recovery are equal. If the name starts to be distressed (that is, if the market prices defaults risk up) then the market start "trading" recoveries on that name, and you have a bid/offer on the recovery such that $\textrm{Notional}\times (1 - \textrm{recovery})$ is going to be payed on default to the protection buyer. The real recovery quoted by Markit on a day $D$ is then a mid recovery (on all contributors to markit) of mid recoveries on bid/offer average of recovery provided by the contributors at the previous business date.