Estimating Default Probability from a Single Five-Year CDS
Summary
The document considers how to estimate default probability when only one CDS tenor is available, using a constant-intensity Poisson model. With several maturities, the questioner would infer probabilities across successive horizons; with only a five-year contract, the suggested simplifying assumption is that the default probability remains constant over the available horizon. This gives a way to form an estimate from limited tenor data, but it does not recover the term structure of default risk.
The response emphasizes that the estimate should be refreshed over time because changing macroeconomic conditions can alter the implied probability. It points to analysis of the iTraxx CDS index as context for building scenarios, and notes that CDS spread data across multiple tenors may be obtainable from other sources. The discussion provides no derivation, calibration formula, or empirical comparison, so it leaves unspecified how to convert spread into probability and how to account for recovery, discounting, or contract details.
Key ideas
- A single five-year CDS can support a constant-intensity default probability estimate when shorter tenor quotes are unavailable.
- The constant probability assumption cannot reveal how default risk varies across the five-year term.
- The implied estimate may change over time as macroeconomic conditions shift.
- Multiple tenor spread data can help estimate a more detailed default-risk term structure.
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Full text
# Extracting Default probability from a single CDS
# Extracting Default probability from a single CDS
I have to find the CDS's default probability using the simplest Poisson Process (intensity constant).
I'm wondering how to get this estimate if I have only a CDS with maturity 5years.
If I had different maturities I could assume, for example, that the PD (probability of default) related to 1 years is that extracted from the CDS 1 y, then the one related to 2 years is extracted from the CDS with 2-years maturity assuming a pd for the first year equal to the one evaluated before(1year PD) and so on.
So, my question is:
if I have just 1 CDS, as, for instance, the case of iTraxx crossover index, can I compute the PD assuming that this probability remains constant throughout the 5 years?
Do alternative solutions exist?
## Answer by Quantopik (score 1)
https://quant.stackexchange.com/a/18719
Yes, you can assume that, since you cannot extract the probability of default for shorter maturity, but for the 5-years only CDS one, because of unavailability of data.
Of course, you'll have to update with shorter frequency your estimate, because the extracted PD will change overtime and the $PD_t$ could be different from $PD_{t+1}$, according to the macroeconomic scenarios will affect the economy.
I suggest you to take a cue from:
> Byström, Hans. "Credit default swaps and equity prices: The iTraxx CDS index market." Working Papers, Department of Economics, Lund University 24 (2005).
to understand how one analyze that kind of index and, consequently, construct the scenarios to which the CDS is exposed and how the extracted PD could change overtime.
Hope this helps.
## Answer by mic (score 1)
https://quant.stackexchange.com/a/21556
It is not a direct answer to your question, but if the real problem is the lack of data, you can check www.datagrapple.com for spreads on the tenors 1, 3, 5, 7 and 10 years for coporate, financial, sovereign CDS and iTraxx / CDX indices.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.