The Impact of Asset Price Bubbles on Credit Risk Measures

Michael Jacobs Jr

doi:10.4236/jfrm.2015.44019

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 both the standard deviation and 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”), a phenomenon that must be taken into consideration for the proper determination of economic capital for both credit risk management and measurement purposes.

Highlights

The financial crisis of the last decade has been the impetus behind a movement to better understand the relative merits of various risk measures, classic examples being Value-at-Risk (“VaR”) and related quantities (Jorion, 2006; Inanoglu & Jacobs, 2009)
The results of our experiment demonstrate that the existence of an asset price bubble, which occurs for certain parameter settings in the Constant Elasticity of Variance (CEV) model, results in the firm asset value distribution having both a lower standard deviation and a greater right skewness
Comparing bubble to non-bubble economies, it has been shown that asset price bubbles may cause an obligor’s traditional credit risk measures to decline, due to a reduced standard deviation and a reduced right skewness of the credit loss distribution

Summary

Introduction

The financial crisis of the last decade has been the impetus behind a movement to better understand the relative merits of various risk measures, classic examples being Value-at-Risk (“VaR”) and related quantities (Jorion, 2006; Inanoglu & Jacobs, 2009). The results of our experiment demonstrate that the existence of an asset price bubble, which occurs for certain parameter settings in the CEV model, results in the firm asset value distribution having both a lower standard deviation and a greater right skewness This augmented right skewness in conjunction with a reduced variance of a firm’s return due to bubble expansion results in a reduction of the right skewness in the distribution of the default rate and a lower PD, which in combination with a lower mean of the LGD process, results in a credit loss distribution having lower mean right skewness and standard deviation. As shown by the additional risk measure proposed in the present paper, the EHPCL, this conclusion is incorrect This credit loss measure increases in bubble economies and is due to bubble bursting, which causes significant firm value losses on the bubble-bursting paths.

Review of the Literature

A Credit Model for Asset Price Bubbles

A Simulation Experiment

Conclusion and Future Directions