Use Observable Credit Spreads for Credit Derivative Risk Statistics

Summary

The discussion asks what market variable should serve as the input to a variance-covariance matrix for a portfolio of credit derivatives such as credit default swaps. The answer recommends basing risk statistics on observable market quantities. For traded CDS, that can mean quoted credit spreads; for traded or marked-to-market debt, it can mean yields in excess of credit-risk-free rates. These measures are tied to market prices and can be monitored over time to estimate variation and co-movement across positions.

Default probabilities are not the suggested substitute for equity returns because physical and risk-neutral probabilities are not directly observable market prices. The exchange is brief and does not prescribe a particular estimation window, spread-change convention, valuation model, or treatment of illiquid instruments. Those choices still matter when constructing a portfolio risk matrix, and the relevant observable depends on what trades or marks are available for the instruments being modeled.

Key ideas

• Build credit derivative risk statistics from observable market variables where possible.
• Quoted CDS spreads can serve as market inputs when CDS instruments trade.
• Bond yields in excess of credit-risk-free rates provide another observable measure of credit risk.
• Default probabilities are model estimates rather than directly observable market prices.
• The discussion does not specify estimation methods or address how to handle sparse or illiquid quotes.

Tags

# Variance covariance matrix for a portfolio of credit derivatives


# Variance covariance matrix for a portfolio of credit derivatives












If the var-covar matrix for equities takes the return on equity prices, what should the var-covar matrix for credit derivatives (like a CDS) take?

Should it be the probability of default, since that usually determines the prices of the credit derivatives?

I'm not sure on what would be the equivalent of equity return for credit derivatives and would appreciate any help on this.

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/70069

As a general principle, you should try to calculate statistics from market observables. Credit spreads are observable. If CDS trades, then you can see CDS quotes. If debt trades or is marked to market, then you can figure out how much they yield in excess of credit risk-fgree rates. But probabilities of default (physical or risk-neutral) are not observable.

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