What is Monte Carlo?
A small principality in Europe. But you knew that. It is a simulation technique. First make some assumptions about the distribution of changes in market prices and rates (for example, by assuming they are normally distributed), then collecting data to estimate the parameters of the distribution). The Monte Carlo then uses those assumptions to give successive sets of possible future realizations of changes in those rates. For each set, the portfolio is revalued. When done, you’ve got a set of portfolio revaluations corresponding to the set of possible realizations of rates. From that distribution you take the 99th percentile loss as the VaR.
