Estimating Default Correlations Using Simulated Asset Values

Abstract

We outline the ingredients necessary to compute the Joint Default Probability from which we obtain Default Correlation, an important risk quantity in the determination of Internal Rating Based Approach in Basel II and III documents on banking supervision and regulations. We discuss Merton’s structural approach of which one key drawback is the difficulty in tracking and calibrating asset value processes and the limitations of variant models which tend to be analytically too complex and compu¬tationally intensive. We address these issues by simulating all the possible asset value processes of a firm whose asset paths we assume to be Gaussian. By generating random values that simulate all the possible asset value processes, we are able to capture all the possible default horizons within a certain macroeconomic framework. Drawing standardised normally distributed assets values of obligors we obtain a range of values of Joint Default Probabilities at a specified asset correlation from which the corresponding range of default correlations are obtained. The results is a simplified approach to the determination of default correlation, easily implementable in Excel and less analytically complicated than existing procedures.