Monte Carlo Importance Sampling Approach To Measuring Portfolio Credit Risk And Its Simulation

The method of Monte Carlo has been widely used for risk management. It plays an important role in this field. However, with the emergence and development of modern portfolio credit risk management perspective, the crude Monte Carlo method can not meet the requirements. In this paper we compute the probability that the total loss of portfolio consisted of the small default probability assets over a larger given loss. In dealing with such small probability, crude Monte Carlo methods will greatly reduce the precision of the simulation. So it is necessary to consider a more adaptable sampling method. This paper trys to use the importance sampling method. Compared to the crude Monte Carlo method,importance sampling method gives more weights to the main reasons for the incident, in this way, the small probability incident can be better captured, so that it can improve the precision of the simulation.This paper considers two kinds of common portfolios credit risk model synthetically, normal latent variable model and extremal dependence model, then realizes the importance sampling algorithms based on these two models. This paper focuses on the comparison of crude Monte Carlo method and importance sampling method under different parameters. Comparing the experimental data came from the Importance sampling methods and the crude Monte Carlo Method, the former was better than the latter in the following three aspects: 1) with the same number of simulations, the standard deviation got from importance sampling is less than the one from crude Monte Carlo Method, which shows that with the same number of simulations, the use of importance sampling method can be more effective in improving the simulation precision than crude Monte Carlo does; 2) Crude Monte Carlo simulation needs far greater number of effective simulations than the importance sampling. So the efficiency of importance sampling method is better than crude Monte Carlo method; 3) when the assets'amount of the portfolio is increased, the rate of precision which depressed with importance sampling method is less than it does with crude Monte Carlo method. Meanwhile importance sampling method can be used in many situations in which crude Monte Carlo method can not get reasonable results. Considering the portfolios credit risk measurement, the use of importance sampling method is superior to crude Monte Carlo method.