Hull, Options, Futures, and Other Derivatives, Chapter 24

[Vicky26]

Vasicek model gives WCDR which is same as 1-V(T,X). Then why are we using V(T,X) while calculating Credit VAR. Formula for credit VAR should be L(1-RR)(1-V(T,X)) rather than L(1-RR)V(T,X). Is there any typo in this or previous slide ?

 

[Clay Carter]

Vasicek model gives WCDR which is same as 1-V(T,X). Then why are we using V(T,X) while calculating Credit VAR. Formula for credit VAR should be L(1-RR)(1-V(T,X)) rather than L(1-RR)V(T,X). Is there any typo in this or previous slide ?

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@Vicky26 The thing to remember is that V(T, X) in Hull's notation is already the WCDR. It is not 1 minus something, it is the worst-case default rate itself at confidence level X. So Credit VaR = L(1-RR) x V(T,X) is just saying worst-case loss = exposure x LGD x worst-case default rate. Totally straightforward once you see it that way.

The confusion usually comes from working through the Vasicek derivation, where you get:

WCDR = N[ (N^-1(PD) + sqrt(rho) x N^-1(X)) / sqrt(1 - rho) ]

That whole thing is V(T, X). It spits out a high default rate at high confidence levels, no extra "1 minus" step needed.

If you used L(1-RR)(1 - V(T,X)) instead, you would be calculating the best-case loss, which is the opposite of what you want.

 

[Vicky26]

In that case why are we doing '1 minus' in formula for V(T,X). It should just be formula for WCDR, and no '1 minus'.