CREDIT RISK OPTIMIZATION VIA CVAR AND ITS SOLUTION

Abstract

Credit risk is the risk of loss stemming from borrower's default. We consider the credit risk minimization problem and propose an optimization method for minimizing the risk measured by Conditional Value-at-Risk (CVaR) criterion. Default of firms is modeled by the corporate valuation model and the factor analysis of time series data of TOPIX Sector Indices, scenarios of defaults are generated, and then CVaR minimization problem is solved. By varying the number of factors incorporated in the model as well as the coefficient that determines the impact of factors peculiar to industry type, we observe how economic trend, industry type and rating of the firms influence the defaults and the credit risk. A large number of scenarios are required to obtain a reliable implication; however, the CVaR minimization problem becomes harder to solve. We propose a simple but effective pre-treatment of the scenarios and also a solution technique. We solved the problem with a hundred thousand scenarios in about 7 seconds and that with half a million scenarios in about 35 seconds.