Credit transition matrix

[Bturtle]

Hi, would someone know what is the rationale behind 'after year 2 and year 3' calculations?

Thank you.

 

[ShaktiRathore]

See the possible states three yrs down the line for A rating is
Default in 1st yr P(D)=0% as A rating has 0% PD in 1yr
Default in 2nd yr can happen when in 1st yr A migrated to B and Default in 2nd yr i.e. BD P(BD)=5%*10% orAD P(AD)=95%*0%=0% u see second is conditional probability dependend on state achived at rating achieved by end of yr1. By second year A would migrate as A->A->B or A->B->B to acheive rating B by 2nd yr P(B in 2 nd yr)=P( A->A->B or A->B->B)= 95%*5%+5%*80%.
Default in 3rd yr can happen BBD(A->B in yr 1 then B->B in yr 2 then B defaults in yr 3) or BAD or ABD or AAD so PD(AAD)=0%=P(BAD),P(BBD)=5%*80%*10%,P(ABD)=95%*5%*10% so PD (3rd yr)= 5%*80%*10%+95%*5%*10%
Thanks

 

[Bturtle]

Thanks Shakit! .