FE-680: Advanced Derivatives
ASSIGNMENT - 5
FALL 2021
SANKALPA AWASTHI
CWID-10474012
Solution 1
The conditional loss distributed of a homogenous independent portfolio of ??? = 100 credits for
?? = {?5, ?3, ?1, ?0.5, ?0.05, 1, 3.5}
Considering the Gaussian latent variable model
NC = 100 credits for Z = {-5, -3, -1, -0.5, -0.05, 1, 3.5}
P ( 2M) = ( 1 / NC ) * ∑ NC i=1 Pi ( 2M)
= ( 1 / 100) * ∑ NC i=1 ((P(-5), P(-3), P(-1), P(-0.05), P(-0.05), P(1), P(3), P(5))
= ( 1 / 100) * P(0.1)
P ( 2M) = 0.01
Conditional Loss distribution = 0.01
Assume on unconditional default probability of 6%
Beta = 30% , R = 30%
The distribution of unconditional loss is
P ( 2M) = (1 / 100) * 0.3 * 0.3
P ( 2M) = 0.0009
SOLUTION 2