I need to apply Basel/Vasicek formula to a 20-years horizon, both from a 20-years cumulative perspective and year-on-year basis.
Please find below the formula of the Basel Capital (ie. unexpected loss):
$$ {\displaystyle K=LGD*\left[N\left({\sqrt {\frac {1}{1-R}}}*G(PD)+{\sqrt {\frac {R}{1-R}}}*G(0.999)\right)-PD\right]} $$
From my understanding there is no issue in it: this limiting formula was derived with no assumption on 1-year horizon.
Am I misunderstand anything? What?
Gratefully.