Simulation of joint default time
Posted: February 17th, 2015, 3:27 pm
Hi, I would like to get some insights on how to simulate default time from bivariate distributions. I was new to copula formula and recently has exposed to bivariate distributions like Marshall Olkin bivariate distributions. It seems like its joint distribution was:[$]Q(\tau^A>x_1, \tau^B>x_2) = exp(- ((\lambda_1x_1)^\theta + (\lambda_2x_2)^\theta )^{1/\theta})[$]If I want to simulate a pair of variable [$](t_1, t_2)[$] from the distribution, do I just simulate the 2 exponential variable and then apply some transformations to them?Also how do I include the correlation of the pair into the simulation? Great if can have some guidelines from you. Thanks.