Consider a portfolio with 30 assets. Denote P(D 8, 1.5y) the probability of

9 or more defaults within the first 18 months; P(D = 0, > 2y) the probability

of zero defaults within the first 2 years, etc.

Generate X

1, X

2, . . . X

30 which are jointly normal distributed variables with

means zero, standard deviations one and correlation 0%, 15% and 35%, respectively. Generate a covariance matrix and compute

X N(0, )

and return Ui = (Xi) where is the univariate cumulative normal distribution

function. Calculate default times ( ) using the following assumptions for the

= 15% and N = 250, 000 simulations. Populate the Gaussian copula default

probabilities in the table below (in percent, 2 decimals).

(ii) Now generate X

1, X

2, . . . X

30 which are jointly Student t distributed random

variables with correlation 0%, 15% and 35%, respectively, and degrees of freedom

= 4. Let Ui = t(Xi) where t is the is the univariate cumulative Student

t distribution function. Again, calculate default times ( ) using the following

assumptions for the = 15% and N = 250, 000 simulations. Populate the tcopula default probabilities in the right hand side of the table below (in percent,

2 decimals).

(iii) Discuss the differences between the results in the table.