Hull, Options, Futures, and Other Derivatives, Chapter 24
- Thread starter Vicky26
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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 The key 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. Pretty 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 expression is V(T,X). It spits out a high default rate at high confidence levels, so no extra "1 minus" step is 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.
