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.
KeywordsFinancial CrisisCredit RiskModel RiskAsset Price BubblesExpected LossCredit Val-Ue-At-RiskStochastic Differential EquationsProbability of DefaultLoss Given DefaultConstant Elasticity of VarianceCox-Ingersoll-Ross
Alexander, C. (2001). Market Models: A Guide to Financial Data Analysis. New York, NY: Wiley.
Araten, M., Jacobs Jr., M., & Varshney, P. (2004). Measuring LGD on Commercial Loans: An 18-Year Internal Study. The Journal of the Risk Management Association, 2, 28-35.
The Basel Committee on Banking Supervision (2005). An Explanatory Note on the Basel II IRB Risk Weight Functions. Basel: Bank for International Settlements.
The Basel Committee on Banking Supervision (2006). International Convergence of Capital Measurement and Capital Standards: A Revised Framework. Basel: Bank for International Settlements.
The Basel Committee on Banking Supervision (2009a). Principles for Sound Stress Testing Practices and Supervision— Consultative Paper.
The Basel Committee on Banking Supervision (2009b). Strengthening the Resilience of the Banking Sector. Bank for International Settlements Consultative Document.
The Basel Committee on Banking Supervision (2010). Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems. Bank for International Settlements.
Back, K. (2010). Asset Pricing and Portfolio Choice Theory. London: Oxford University Press.
Chan, K. C., Karolyi, G. A., Longstaff, F. A., & Saunders, A. B. (1992). An Empirical Comparison of Various Models of the Short Term Interest Rate. Journal of Finance, 47, 1209-1227. http://dx.doi.org/10.1111/j.1540-6261.1992.tb04011.x
Cornford, A. (2005). Basel II: The Revised Framework of June 2004(Technical Report). New York: United Nations Conference on Trade and Development.
Delbaen, F., & Schachermayer, W. (1995). Arbitrage Possibilities in Bessel Processes and Their Relations to Local Martingales. Probability Theory and Related Fields, 102, 357-366. http://dx.doi.org/10.1007/BF01192466
Delbaen, F., & Schachermayer, W. (1998). The Fundamental Theorem of Asset Pricing for Un-Bounded Stochastic Processes. Mathematische Annalen, 312, 215-250. http://dx.doi.org/10.1007/s002080050220
Development Core Team (2015). R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
Emanuel, D. C., & MacBeth, J. D. (1982). Further Results on the Constant Elasticity of Variance Call Option Pricing Model. Journal of Financial and Quantitative Analysis, 17, 533-554. http://dx.doi.org/10.2307/2330906
Embrechts, P., McNeil, A. J., & Straumann, D. (1999). Correlation: Pitfalls and Alternatives. Risk, 12, 69-71.
Embrechts, P., McNeil, A. J., & Straumann, D. (2002). Correlation and Dependence in Risk Management: Properties and Pitfalls. In M. A. H. Dempster (Ed.), Risk Management: Value at Risk and Beyond (pp. 176-223). Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511615337.008
Embrechts, P., Lindskog, F., & McNeil, A. J. (2003). Modeling Dependence with Copulas and Applications to Risk Management. In: S. Rachev (Ed.), Handbook of Heavy Tailed Distributions in Finance (pp. 329-384). Rotterdam: Elsevier. http://dx.doi.org/10.1016/B978-044450896-6.50010-8
Engelmann, B., & Rauhmeier, R. (2006). The Basel II Risk Parameters. New York: Springer. http://dx.doi.org/10.1007/3-540-33087-9
Frey, R., & McNeil, A. J. (2001). Modeling Dependent Defaults. Working Paper, ETH Zurich.
Frye, J., & Jacobs Jr., M. (2012). Credit Loss and Systematic LGD. The Journal of Credit Risk, 8, 109-140.
Hong, H., Scheinkman, J., & Xiong, W. (2006). Asset Float and Speculative Bubbles. Journal of Finance, 61, 1073-1117. http://dx.doi.org/10.1111/j.1540-6261.2006.00867.x
Inanoglu, H., & Jacobs Jr., M. (2009). Models for Risk Aggregation and Sensitivity Analysis: An Application to Bank Economic Capital. The Journal of Risk and Financial Management, 2, 118-189. http://dx.doi.org/10.3390/jrfm2010118
Jacobs Jr., M. (2001). A Comparison of Fixed Income Valuation Models: Pricing and Econometric Analysis of Interest Rate Derivatives. PhD Thesis, New York: The Graduate School and University Center of the City University of New York.
Jacobs Jr., M. (2011). A Two-Factor Structural Model of Ultimate Loss-Given-Default: Capital Structure and Calibration to Corporate Recovery Data. The Journal of Financial Transformation, 31, 31-43.
Jacobs Jr., M. (2012). An Option Theoretic Model for Ultimate Loss-Given-Default with Systematic Recovery Risk and Stochastic Returns on Defaulted Debt. Proceeding of the 2010 3rd Annual Joint Bank for International Settlements— World Bank—European Central Bank Public Investors Conference, BIS Paper No. 58 (October), 257-285.
Jacobs Jr., M. (2013). Stress Testing Credit Risk Portfolios. The Journal of Financial Transformation, 37, 53-75.
Jacobs Jr., M., & Karagozoglu, A. K. (2011). Modeling Ultimate Loss Given Default on Corporate Debt. The Journal of Fixed Income, 21, 6-20. http://dx.doi.org/10.3905/jfi.2011.21.1.006
Jacobs Jr., M., & Kiefer, N. M. (2010). The Bayesian Approach to Default Risk: A Guide. In K. Boecker (Ed.), Rethinking Risk Measurement and Reporting (pp. 1-30). London: Risk Books.
Jacobs Jr., M., Karagozoglu, A. K., & Sensenbrenner, F. J. (2015). Stress Testing and Model Validation: Application of the Bayesian Approach to a Credit Risk Portfolio. The Journal of Risk Model Validation, 9, 41-70.
Jarrow, R. A., & Protter, P. (2010). The Martingale Theory of Bubbles: Implications for the Valuation of Derivatives and Detecting Bubbles. In A. Berd, (Ed.), The Financial Crisis: Debating the Origins, Outcomes, and Lessons of the Greatest Economic Event of Our Lifetime (pp. 429-448). New York: Risk Publications.
Jarrow, R. A., Protter, P., & Shimbo, K. (2007). Asset Price Bubbles in Complete Markets. In M. C. Fu, R. A. Jarrow, J. Y. J. Yen, & R. J. Elliott (Eds.), Advances in Mathematical Finance (pp. 97-121). New York: Springer. http://dx.doi.org/10.1007/978-0-8176-4545-8_7
Jarrow, R. A., Protter, P., & Shimbo, K. (2010). Asset Price Bubbles in Incomplete Markets. Mathematical Finance, 20, 145-185. http://dx.doi.org/10.1111/j.1467-9965.2010.00394.x
Jarrow, R. A., Kchia, Y., & Protter, P. (2011). How to Detect an Asset Bubble. SIAM Journal on Financial Mathematics, 2, 839-865. http://dx.doi.org/10.1137/10079673X
Jarrow, R. A., & Silva, F. B. G. (2014). Risk Measures and the Impact of Asset Price Bubbles. The Journal of Risk, 17, 145-185.
Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical Methods for Financial Markets. In P. Jorion (Ed.), Value at Risk: The New Benchmark for Controlling Market Risk (Vol. 2, pp. 69-93). New York: McGraw-Hill. http://dx.doi.org/10.1007/978-1-84628-737-4
Jorion, P. (1999). Value at Risk: The New Benchmark for Controlling Market Risk (Volume 2). New York: McGraw-Hill.
Jorion, P. (2006). Value at Risk: The Benchmark for Managing Financial Risk (3rd ed.). New York: McGraw Hill.
Li, D. X. (2000). On Default Correlation: A Copula Function Approach. Journal of Fixed Income, 9, 43-54. http://dx.doi.org/10.3905/jfi.2000.319253
Merton, R. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance, 29, 449-470.
Øksendal, B. K. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Berlin: Springer. http://dx.doi.org/10.1007/978-3-642-14394-6
Poon, S. H., Rockinger, M., & Tawn, J. (2004). Extreme Value Dependence in Financial Markets: Diagnostics, Models and Financial Implications. Review of Financial Studies, 17, 581-610. http://dx.doi.org/10.1093/rfs/hhg058
Protter, P., & Shimko, K. (2010). Risk Measures and the Impact of Asset Price Bubbles. Journal of Risk, 17, 35-55.
Schroder, M. (1989). Computing the Constant Elasticity of Variance Option Pricing Formula. Journal of Finance, 44, 211-219. http://dx.doi.org/10.1111/j.1540-6261.1989.tb02414.x
Sklar, A. (1956). Fonctions de Répartition à NDimensions et Leurs Marges. Publications de l’Institut de Statistique de L’Université de Paris, 8, 229-231.
The US Board of Governors of the Federal Reserve System (2011). Supervisory Guidance on Model Risk Management (FR 2011-12). Washington DC: The US Board of Governors of the Federal Reserve System.