I'm new to this forum and new to the world of financial risk management. I need to build a Value at Risk model for three foreign currencies. I have had no trouble setting up the univariate models using GARCH(1,1) but I am having trouble setting up the multivariate case. For example, I found a book that uses a formula for a "correlated random price change" as the sum over assets i (currencies) where X_k=Sqrt(lambda_i) x X_norm x nu_ki x sigma_k , where X_k = correlated return for currency with a normal distribution and the volatility of the currency sigma_k = volatility of currency through the GARCH process Sqrt(lambda_i) = square root of the eigenvalue for the currency i X_norm = random return change from a normal distribution (NORMSINV(RAND(),0,1)nu_ki = the kth element of the eigenvector for the ith currencybut I have no clue where this came from. Does anyone have a reference I could use? Is there a better way?I found a source that told me how to dynamically calculate a new correlation matrix but I would hate to have to build the code to generate eigenvalues for each Monte Carlo iteration for each day!Many thanks.

Sorry as I just found out how to post an equation. The equation I crudely posted above is actually:

search on here & google for principal component analysis.

Thanks Mutley. Just what I needed. One question: Would you agree that the methodology is sound for generating a multivariate model, or is there a better way?