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Credit VaR and the Gaussian Default-Rate Quantile

Article Quant Q&A · Author: AfterWorkGuinness
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Summary

The document discusses Hull’s formula for estimating a portfolio’s high-confidence default rate over a fixed horizon. It applies the inverse normal distribution to the probability of default and confidence level, with asset correlation entering through a Gaussian copula framework. The estimated default rate is then multiplied by portfolio value and loss given default to obtain the stated credit VaR measure.

The question contrasts this measure with unexpected loss, often expressed as a tail loss less expected loss. The reply says these are distinct concepts: Hull’s calculation is credit VaR, while the alternative being considered concerns credit risk capital requirements. The exchange offers no worked derivation or broader comparison, so it is a brief conceptual clarification rather than a full treatment of credit risk measurement.

Key ideas

  • The formula estimates a high-confidence default rate using default probability, correlation, and a confidence level.
  • Portfolio value and loss given default scale the estimated default rate into a credit loss measure.
  • The response distinguishes credit VaR from credit risk capital requirements.
  • The document does not provide a derivation or detailed comparison of the measures.

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Fixed incomeRisk managementStatistics
Full text
# How to calculate Credit VaR?


# How to calculate Credit VaR?












(source John Hull, Options Futures and Other Derivatives 8th edition)

I can't follow why Hull calculates Credit VaR in the following manner. I thought CVaR was Unexpected Loss$_{confidence}$ - Expected Loss.

Hull calculates the 1 year 99.9% worst case default rate as:

$V(confidence,T) = N(\frac{N^{-1}(PD)+(\sqrt{p}) N^{-1}(confidence)}{\sqrt{p}})$

CVaR = portfolio value * $V(confidence, T)$ * Loss Given Default

(in the given example, he get correlation (P) via a Guassian copula)

## Answer by Egodym (score 1)

https://quant.stackexchange.com/a/20654

You are confusing C-VaR and capital requirements for the credit risk of a counterparty. C-VaR is given by the Hull's formula you wrote, whereas what you call "Malz approach" is the calculation of the capital requirements. Check Hull - Risk Management and Financial Institutions p. 341.

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