An Efficient Monte Carlo Method for a Large and Nongranular Credit Portfolio

by Hideaki Higo of the Bank of Japan

November 2006

Abstract: It can be time consuming to evaluate the risk of a large credit portfolio with Monte Carlo simulation. This paper introduces a simple yet efficient Monte Carlo method where the portfolio is divided into subportfolios of obligors with large exposures and those with small exposures. Neglecting the idiosyncratic risks in the latter subportfolio, an approximation of value-at-risk for the entire portfolio is obtained in a short time. The new method is tested using sample portfolios of nongranular 5,000 exposures. The technique provides accurate credit value-at-risk with a computation time about one-fifteenth of ordinary Monte Carlo simulation. In addition to the improved computational efficiency, the method can also be used to specify the range of a subportfolio where idiosyncratic risks do not contribute to the value-at-risk of the entire portfolio. This may serve as important information when senior credit managers review the appropriateness and efficiency of internal risk management systems from the viewpoint of obligor's risk contribution.

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