# Recovery

The Recovery of a Credit Event is used in two main situations, Pricing and Settlement.

## Recovery Assumption - Pricing

When pricing Credit Derivatives it is almost impossible to escape the Recovery Assumption when building a pricing model.

The discounting models will have a discount factor linked to the probability of survival, that is obviously one of the major unknowns in the market however given the price of a bond (or a credit derivative) one can work out the market price implied survival probability, however this cannot be done without making some kind of guess as to the price of an asset after a default has occurred.

An example of how this relationship behaves can be illustrated as follows:

Imaging a distressed zero coupon bond which is trading at a price of 80 and has a month to maturity - i.e. no cashflows are due other than the principal payment and there's little effect of the time value of money.

If you assume that the recovery of this bond would be 0 then there's a long way for this bond to fall before it would default.

• If the bond survives you would make 20 as it would redeem at par (100)
• If the bond defaults you would lose 80

Using a fair/efficient market assumption the probability of survival Ps satisfies this equation:

```20 * Ps = 80 * (1 - Ps)
```

This would imply an 80% chance of survival (or 20% probability of default).

Now let's say that actually the entity issuing this bond has a lot of assets that would be sold in a default and actually the bond wouldn't go to zero but would in fact trade more like 50, this is much closer to the current price and therefore the probability of survival is a lot lower:

• If the bond survives you would make 20 as it would redeem at par (100)
• If the bond defaults you would lose 30

Using a fair/efficient market assumption the probability of survival Ps satisfies this equation:

```20 * Ps = 30 * (1 - Ps)
```

Now this implies a 60% probability of survival (or 40% probability of default).

The Recovery Assumption is used in pricing of credit derivatives and is only relevant before the Auction process has happened

During the early years of CDS trading there was no market standard about what recovery should be used when calculating fees for unwinds (see Pricing page for more information), in fact some dealers would charge a bid/offer not only on the CDS itself but also a bid/offer on the recovery assumption when working out the final fee. This didn't go down well and it was agreed that for calculation of fees there would be market standard assumed recoveries and that only the bid offer on the CDS would be applied.

These ISDA standard assumptions can be found at the CDS model page.

## Final Price - post-Auction Recovery for Settlement

Once a Credit Event has been officially determined an Auction Process begins, originally designed to be Physical Settlement, now Credit Default Swaps almost always trade with Cash Settlement. That amount is calculated as the Notional of the trade multiplied by (100 - Final Price)%.

Following the Big Bang protocol market participants agreed to a standardised Auction mechanism to determine the Final Price, buyers of protection still have the option to deliver bonds (or loans) into the contract or to sell into the auction, but for those who only want cash settlement the process is clean and transparent.