# 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)

• Why do you think it should be calculated differently from Hull's formula? – Egodym Sep 6 '15 at 16:25
• I thought credit var is unexpected loss = 99.9% quantile - Expected Loss where expected loss = pdeadlgd – AfterWorkGuinness Sep 6 '15 at 17:16
• What is the reference for your statement? – Egodym Sep 6 '15 at 17:29
• Malz cites this approach. I think one of the BIS papers does too. I dont have the source handy. – AfterWorkGuinness Sep 6 '15 at 17:37