Separating Credit Spread Risk from Default Risk in Risk Models

# Dependence between Credit Default Risk and Credit Spread Risk


# Dependence between Credit Default Risk and Credit Spread Risk












I am trying to understand the difference and similarities between Credit Spread Risk and Credit Default Risk.

Here is brief (and not all too precise) definition.





For simplicity sake, lets consider a portfolio which consists of a single zero-coupon bond.

Credit Spread Risk deals with changes in credit spreads. One of the main reasons why the Credit Spread of our bond might change is that market participants believe that the available information on potential future losses has changed. But this risk is also included in the definition of credit default risk.

I was wondering if to a certain degree these two risk definitions overlap and whether there are methods to quantify this overlap. So for example assume that for this particular bond we have that

- Credit-Spread-VaR = 200

- Credit Default UL = 100

Do you know any methods on how to quantify the overlap? Or put differently, do you know any methods to analyse if these figures include any kind of double counting of risks?

The way I see it (as of now) Credit Default Risk should to a large extend be included in Credit Spread Risk.

Thank you.

## Answer by Kermittfrog (score 2, accepted)

https://quant.stackexchange.com/a/65578

Commonly, the definition of credit risk is the risk that, over a given time horizon, at a certain confidence level, names in our credit portfolio deteriorate or even default, leading to a (present value) loss. Commonly, this risk is not marked-to-market (most of our credit is not tradeable) and the risk horizon is 1 year. As you already noted, the risk is $UL$-$EL$; and the expected loss plus a tail risk provision has already been factored into the credit conditions / margin requirements.

The overlap between credit spread risk and credit risk is driven by the model(s) you use:

Disregarding interest rate risk, the effects of interim cash flows and time effects, an integrated risk model would consider the following:

- gains / losses due to credit migration, with a revaluation of the position at 'new', corresponding credit spreads

- gains / losses due to credit spread movements (given non-default).

- losses due to jump to default

Commonly, the credit risk model only covers 1 + 3, whereas the credit spread risk model covers 2 and parts of 1.

### Where is the overlap?

The magic is in the calibration of the credit spread risk factor you use in either of these models. Without going too much into the details:

- credit spread risk factors must be calibrated somehow, commonly using observed spread series; e.g. thru credit spread index series, rating/sector series, single name series - whatever is available (in your shop's terminals) and liquid. Some places even calculate their own credit spread series (...the horror!)

- observed series may be polluted by credit effects, e.g. there may be jumps in spreads that were induced by a true credit event (imminent or 'pre-visible' rating downgrade) - and these jumps will directly enter your credit spread risk components.

In a textbook world, we would calibrate the credit spread risk components in either model (credit,credit spread, integrated risk) based on a series of credit spreads that does not contain jumps due to credit events. Then, there would be no overlap between the two risks; in an integrated risk model, at least.

HTH?

## Answer by Mild_Thornberry (score 1)

https://quant.stackexchange.com/a/65505

Credit spread risk is a risk-neutral probability of default. That is, it includes the expected loss plus a systemic risk premium if one ignores factors like liquidity, counterparty risk, and tax effects. Other posts in this page show how one can calculate a risk-neutral probability of default given CDS spreads.

CDS Spread = EL + RP

Credit risk is a real-world probability normally calculated using something like Merton’s distance to default probability. As long as investors are risk-averse, your risk-neutral default probability will always be greater than your real world default probability, because it only captures the EL component of credit spread risk and your RP is positive.

By quantifying distance to default probability, you have already quantified the overlap between credit spread risk and credit risk.