# Multi-period Basel/Vasicek formula

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):

$$K=LGD*\left[N\left({\sqrt {\frac {1}{1-R}}}*G(PD)+{\sqrt {\frac {R}{1-R}}}*G(0.999)\right)-PD\right]}$$

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.

• If the objective is cumulative losses over 20 years without regard to movements over the individual years then don’t see any complication as long as the parameters reflect the 20 years horizon. If the objective is multi year modelling then complementing the one year with migration matrices is more pragmatic Aug 18 '20 at 21:23
• What is, and could you provide, the Basel/Vasicek formula in your question Aug 19 '20 at 5:47
• @Magicisinthechain you mean, for cumulative losses you only need to use 20years-parameters, while for year-on-year you should consider the 1year-parameters + the migration. Is it correct? Aug 19 '20 at 8:04
• Yes that’s right thanks! Aug 19 '20 at 11:06