Asset price bubbles and the quantification of credit risk capital with sensitivity analysis, empirical implementation and an application to stress testing

Abstract

This study presents an analysis of the impact of asset price bubbles on standard credit risk measures, including Expected Loss (“EL”) and Credit Value-at-Risk (“CVaR”). We present a styled model of asset price bubbles in continuous time, and perform a simulation experiment of a 2 dimensional Stochastic Differential Equation (“SDE”) system for asset value determining Probability of Default (“PD”) through a Constant Elasticity of Variance (“CEV”) process, as well as a correlated a Loss-Given-Default (“LGD”) through a mean reverting Cox-Ingersoll-Ross (“CIR”) process having a long-run mean dependent upon the asset value. Comparing bubble to non-bubble economies, it is shown that asset price bubbles may cause an obligor’s traditional credit risk measures, such as EL and CVaR to decline, due to a reduction in the right skewness of the credit loss distribution. We propose a new risk measure in the credit risk literature to account for losses associated with a bubble bursting, the Expected Holding Period Credit Loss (“EHPCL”). We present evidence that asset price bubbles are a phenomenon that must be taken into consideration in the proper determination of economic capital for both credit risk management and measurement purposes. We also perform a sensitivity analysis of the SDE parameters upon the resulting credit risk measures, as well as the changes in their relationship to the CEV parameter, illustrating an application of an important model validation procedure.