An Analytical Value-at-Risk Approach for a Credit Portfolio with Liquidity Horizon and Portfolio Rebalancing

Abstract

We provide a two-period analytical value-at-risk (VaR) approach for the credit portfolio with liquidity horizon and the constant level of risk. Given any time horizon, a two-period credit portfolio loss model is derived and, at the end of the first period, the portfolio is rebalanced to ensure a constant level risk of the portfolio measured by the credit rating. The analyticalVaR is found by extending the granularity adjustment (GA) approximation. The model is applied to incremental risk charge (IRC), with the liquidity horizon of each asset being six months. By testing with the Monte Carlo simulation model, it is shown that the accuracy of the analytic model is acceptable over a large range of parameters. The model behaves similarly to the standard GA in capturing the concentration risk. We also show the features of liquidity horizon and constant level of risk are captured adequately in the model. Our analytical approach behaves better than the standard one-period asymptotic single-risk-factor model with and without GA, to achieve a comparable measure to the IRC.

Keywords: analytical value-at-risk, granularity adjustment, incremental risk charge, portfolio rebalancing, liquidity horizon