Financial Risk Management

Abstract

where Φ (x) is the distribution function of univariate standard normal distribution while Φ2 (x, y; ρ) is the distribution function of the bivariate standard normal distribution with correlation ρ. Let (X1, X2) be a random Gaussian vector of distribution Φ2. Show that the copula of (X1, X2) is the same with the one of the random vector (Φ (X1) ,Φ(X2)). Deduce an algorithm to simulate the Gaussian copula of parameter ρ.