Question

Suppose Apic Bank  lends 1 million to Ken and 5 million to Kiptoo. The probability of default in the first year for Ken is 0.2 and for Kiptoo is 0.3. The probability of joint default (both Ken and Kiptoo default) in 1 year is 0.1. The loss given default (LGD) is 40% for Ken and 60% for Kiptoo. What is the expected loss of default in 1 year for the Apic Bank?

Answer 1

Solution Let X be the event that Ken defaults in 1 year and Y be the event that Kiptoo defaults in 1 year. 

Then P_rX_C|Y_C= 1-P_rX_jY=1-P_rX-P_rY+P_rX_JY

                       = {1-0.2-0.3+0.1}

                        =0.6

and

           P_rX_jY_c = P_rX -P_rX_jY = 0.2-0.1 = 0.1

           P_rY_jX_c = P_rY - P_rY_jX = 0.3-0.1 = 0.2
           P rX_jY = 0.1

Thus the expected loss in one year is given by

0.6(0) + (1) (0.4) (0.1) + 5(0.6) (0.2) + [(1) (0.4) + 5(0.6)] (0.1) = 0.98 million 

 

The expected loss for the Apic Bank in one year is 0.98 Million.