So I wanted to generate a Monte Carlo simulation for two correlated assets to derive then the VaR as a quantile of the generated distributions. My code is the following, where the input parameters are correlation = 1, yearly volatility of both asset 30% and the starting prices are 100 for asset 1 and 80 for asset 2:
SDAsset1 = 0.3 SDAsset2 = 0.3 Corr = 1 Cov = SDAsset1*SDAsset2*Corr cov_matrix <- matrix(c(SDAsset1^2, Cov, Cov, SDAsset2^2), nrow = 2) cov_matrix mu = c(0,0) x<- mvrnorm(100000, mu,cov_matrix) return1 <- x[,1] return2 <- x[,2] asset1 <- exp(return1)*100 asset2 <- exp(return2)*80 quantile(asset1, 0.9) quantile(asset2, 0.9)
My question is now how would I have to change the code and parameters such that I could get the distribution after 1/2 year. My approach would be to take the volatility and divide it by the square root of 2, but I'm not sure where I would have to change the time step.