How Survival Curves Relate to Observable CDS Spreads

Summary

The document explains why a survival curve does not make CDS market quotes redundant. Survival probabilities and hazard rates are not directly observable, while market-standard CDS quotes are. A curve is therefore calibrated by deriving risk-neutral default probabilities or hazard rates from those quotes, using assumptions about recovery and interest rates.

Once a curve is available, it can be used to calculate a par spread for a CDS. That derived spread is distinct from the market-standard quote used to build the curve, so the answer recommends checking whether the application needs a calculated par spread or should use standard quotes directly. The brief exchange gives no calibration equations or examples, and its guidance depends on the quote convention and assumptions used.

Key ideas

• CDS quotes are observable market inputs, while risk-neutral survival probabilities and hazard rates are inferred quantities.
• A survival curve can be calibrated from CDS quotes using recovery and interest rate assumptions.
• A par CDS spread can be derived from an established survival curve.
• Market-standard CDS quotes and derived par spreads may differ, so the appropriate measure depends on the task.

Tags

# Why do we implement a function to obtain the par spread of a CDS when we have the survival curve?


# Why do we implement a function to obtain the par spread of a CDS when we have the survival curve?












I've been told that a function that determines the par spread of a CDS via the survivorship curve is used to calibrate the survivorship curve. But I don't understand how it can be used for that when we already have the survivor curve as a parameter?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/82229

Problem is, probabilities/hazard rates are not directly observable - neither risk-neutral, not physical/actual. Only CDS quotes are observable.

You derive risk-neutral probabilities/hazard rates from the observable market-standard CDS quotes (using some recovery assumptions and also interest rates). You use the probabilities to price.

If you really need "par" CDS spreads, you can derive them from risk-neutral probabilities/hazard rates. But I suggest you double-check whether you can use market standard quotes rather than par spreads.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.