Monte Carlo Simulation in the Integrated Market and Credit Risk Portfolio Model

Estimation of risk of the large portfolios of credit risky securities is the problem that can be studied using Monte Carlo methods. The main difficulties include the large number of risk factors (interest rates, fx rates, ...) and statistical dependencies between probabilities of default and market risk factors. There are several variance reduction techniques (importance sampling, stratifies sampling, ...) that are applicable to many practical problems in finance, in particular, in pricing of sophisticated securities. The problem is how to use these techniques for portfolio risk analysis. The most interesting practical case corresponds to credit risky portfolios. In this case the portfolio losses depend on default events that are relatively rear. Therefore, efficient Monte Carlo simulation could be based on a transformation of the measure that describes joint evolution of market and credit risk factors.