The size of the default leg is driven by the recovery rate and that this is determined by the post default bond price.

But how exactly is that determined? Firstly, it is important to realize why we don't use the formal recovery rate found by a bankruptcy process.

This final decision as to how much each class of creditors recover can take years to determine if this final recovery rate was used in CDS contracts, then there would be an unacceptable delay between the bond holder experiencing a loss on Declaration of accredit event, and the CDS paying out instead, CDS contracts pay out based on a market implied recovery rate given to us by the price the post default bonds are trading at in the market.

This way, the pay can be calculated and paid in a short timeframe.

In fact, not only is this more convenient, but it is also better for the buyer who is using the CDS as insurance because their loss is driven not by some future recovery rate, but by the immediate drop in the market price of the bond they own.

Their loss is therefore based on the market's implied recovery rate, and it is therefore correct that the CDS payout should be based on the same market implied rate.

In order to discover the market implied recovery rate, an auction is held for the post default bonds.

Market makers put prices into the auction alongside anyone else who would like to buy or sell the bonds, and an auction clearing price is calculated.

This price then sets the recovery rate for the CDS payouts.