Explanation of Vasicek Model??

[gsarm1987]

Hi @David Harper CFA FRM

Could you please explain why N^-1 (PD) has a negative Z value and the N^-1(0.999) has a positive Z value?

Two tailed distribution. Will give positive and negative. .999 is area under the curve, which is the probability. Probabilities less than 0.5 correspond to negative values. You may draw a bell curve, zero (mean) in the middle. I hope it will make sense. Let me know

 

[gsarm1987]

@gsarm1987 Thank you for your kind response!
when F is high my calculation returns a smaller U ( negative ) - and NORMDIST return a smaller PD.
when F is low my calculation returns a larger U ( positive ) and NORMDIST returns a larger PD.

e.g.
correlation = 0.4, PD=1.5%

negative ( low ) F of -3 = ~ 99.9% confidence has a U of -0.27 and that evaluates to 39% PD
for a larger ( high ) F of -1 = ~ 84% confidence has a U of -1.98 = 2.36% PD

I have edited my reply to clarify that high F means implies low PD, because good economic conditions would mean low PD. Also note, in default rate calculated under vasicek, you'll see that F variable has a minus sign.