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(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)

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  • $\begingroup$ Why do you think it should be calculated differently from Hull's formula? $\endgroup$ – Egodym Sep 6 '15 at 16:25
  • $\begingroup$ I thought credit var is unexpected loss = 99.9% quantile - Expected Loss where expected loss = pdeadlgd $\endgroup$ – AfterWorkGuinness Sep 6 '15 at 17:16
  • $\begingroup$ What is the reference for your statement? $\endgroup$ – Egodym Sep 6 '15 at 17:29
  • $\begingroup$ Malz cites this approach. I think one of the BIS papers does too. I dont have the source handy. $\endgroup$ – AfterWorkGuinness Sep 6 '15 at 17:37
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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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  • 1
    $\begingroup$ Thanks. After more digging, I've come across both the method Hull uses and the one Malz describes .."The standard definition of credit Value-at-Risk is cast in terms of UL (Unexpected Loss) : It is the worst case loss on a portfolio with some specific confidence level over a specific holding period, minus the expected loss". $\endgroup$ – AfterWorkGuinness Sep 7 '15 at 18:00
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    $\begingroup$ Further found this definition from the BIS paper An Explanitory Note on the Basel II Risk Weight functions .. "The likelihood that losses will exceed the sum of Expected Loss (EL) and Unexpected Loss (UL) - i.e. the likelihood that a bank will not be able to meet its own credit obligations by its profits and capital - equals the hatched area under the right hand side of the curve. 100% minus this likelihood is called the confidence level and the corresponding threshold is called Value-at-Risk (VaR) at this confidence level" Not questioning Hull, just trying to understand it. $\endgroup$ – AfterWorkGuinness Sep 7 '15 at 18:08
  • $\begingroup$ @AfterWorkGuinness don't hesitate to accept/vote up answers if you're satisfied. $\endgroup$ – SRKX Oct 7 '15 at 2:08
  • $\begingroup$ Hi Srkx, i will when i get a chance to review it in a day or so. $\endgroup$ – AfterWorkGuinness Oct 7 '15 at 2:34

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