Abstract
Stress testing is used to determine the stability or the resilience of a given financial institution by deliberately submitting the subject to intense and particularly adverse conditions which has not been considered a priori. This exercise does not imply that the entity’s failure is imminent, though its purpose is to address and prepare this potential failure. Consequently, as the focal point is a concept (Risk) the stress testing is the quintessence of risk management. In this chapter we focus on what may lead a bank to fail and how its resilience can be measured. Two families of triggers are analysed: the first stands in the impact of external (and/or extreme) events, the second one stands on the impacts of the choice of inadequate models for predictions or risks measurement; more precisely on models becoming inadequate with time because of not being sufficiently flexible to adapt themselves to dynamical changes. The first trigger needs to take into account fundamental macro-economic data or massive operational risks while the second trigger deals with the limitations of the quantitative models for forecasting, pricing, evaluating capital or managing the risks. It may be argued that if inside the banks-limitations, pitfalls and other drawbacks of models used were correctly identified, understood and handled, and if the associated products were correctly known, priced and insured, then the effects of the crisis may not have had so important impacts on the real economy. In other words, the appropriate model should be able to capture real risks (including in particular extreme events) at any point in time, or ultimately a model management strategy should be considered to switch from a model to another during extreme market conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In October 2012, U.S. regulators unveiled new rules expanding this practice by requiring the largest American banks to undergo stress tests twice per year, once internally and once conducted by the regulators.
- 2.
\( VaR_{\alpha} (X) = q_{1-\alpha}= F_{X}^{-1}(\alpha)\).
- 3.
A low number of degrees of freedom imply a higher dependence in the tail of the marginal distributions.
- 4.
- 5.
The maturity adjustment is not always present as it is contingent to the type of credit.
- 6.
Note that the ES obtained from the NIG is far superior to the initial investment, but is still consistent regarding a continously coumpounded portfolio.
- 7.
This section presents the methodologies applied to weekly time series, as presented in the result section. They have also been applied to monthly time series.
- 8.
Maximum Likelihood Estimation.
References
Acerbi, C. and D. Tasche. 2002. On the coherence of expected shortfall. Journal of Banking and Finance 26 (7): 1487–1503.
Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath. 1999. Coherent measures of risk.Mathematical Finance 9 (3): 203–228.
Barndorff-Nielsen, O., and C. Halgreen. 1977. Infinite divisibility of the hyperbolic and generalized inverse gaussian distributions.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 38 (4): 309–311.
BCBS. 2006.Basel committee: International convergence of capital measurement and capital standards. Basel: Bank for International Settlements.
Bedford, T., and R. M. Cooke. 2001. Probability density decomposition for conditionally dependent random variables modeled by vines.Annals of Mathematics and Artificial Intelligence 32:245–268.
Beran, J. 1994.Statistics for long-memory processes. New York: CRC Press.
Berg, D., and K. Aas. 2009. Models for construction of multivariate dependence-a comparison study.The European Journal of Finance 15:639–659.
Berkowitz, J. 1999.A coherent framework for stress testing. Washington DC: Federal Reserve Board.
Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity.Journal of Econometrics 31 (3): 307–327.
Brechmann, E. C., C. Czado, and K. Aas. 2010. Truncated regular vines in high dimensions with applications to financial data. Canadian Journal of Statistics 40 (1): 68–85.
Brockwell, P., and R. Davis. 1988. Simple consistent estimation of the coefficients of a linear filter.Stochastic Processes and Applications 28 (1): 47–59.
Bunn, P., A. Cunningham, and M. Drehmann. 2005. Stress testing as a tool for assessing systemic risks.Financial Stability Review 18:116–126. (Bank of England Stability Review).
Capéraà, P., A. Fougères, and C. Genest. 2000. Bivariate distributions with given extreme value attractor.Journal of Multivariate Analysis 72:30–49.
Caputo, A. 1998. Some properties of the family of koehler-symanowski distributions. Working paper, The collaborative research center (SBF), LMU-München.
Cleveland, W. 1979. Robust locally weighted regression and smoothing scatterplots.Journal of the American Statistical Association 74 (368): 829–836.
Dissmann, J., E. Brechmann, C. Czado, and D. Kurowicka. 2013. Selecting and estimating regular vine copulae and application to financial returns. Statistics & Data Analysis, Elsevier.
Engle, R. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation.Econometrica 50 (4): 987–1007.
Fayyad, U., G. Piatetsky-Shapiro, and P. Smyth. 1996. From data mining to knowledge discovery in databases.AI Magazine 17 (3): 37–54.
Galambos, J. 1978.The asymptotic theory of extreme order statistics. Wiley Series in Probability and Mathematical Statistics. Chichester: Wiley.
Genest, C., K. Ghoudi, and L.-P. Rivest. 1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions.Biometrika 82:543–552.
Gourier, E., W. Farkas, and D. Abbate. 2009. Operational risk quantification using extreme value theory and copulas: From theory to practice.Journal of Operational Risk 3 (2009): 1–24.
Gregory, J. 2012.Counterparty credit risk and credit value adjustment: A continuing challenge for global financial markets, 2nd ed. London: Wiley.
Guégan, D., B. Hassani, and C. Naud. 2011. An efficient threshold choice for the computation of operational risk capital.The Journal of Operational Risk 6 (4): 3–19.
Guégan, D., B. Hassani, and X. Zhao. 2013.Emerging countries sovereign rating adjustment using market information: Impact on financial institutions investment decisions. Oxford: Academic Press.
Guégan, D. 2005. How can we define the concept of long memory? An econometric survey.Econometric Review 24 (2): 113–149.
Guégan, D., and B. K. Hassani. 2009. A modified panjer algorithm for operational risk capital computation.The Journal of Operational Risk 4:53–72.
Guégan, D., and B. Hassani. 2012a. A mathematical resurgence of risk management: An extreme modeling of expert opinions. To appear in Frontier in Economics and Finance, Documents de travail du Centre d’Economie de la Sorbonne 2011.57 - ISSN: 1955-611X.
Guégan, D., and B. Hassani. 2012b. Operational risk: A basel ii++ step before basel iii.Journal of Risk Management in Financial Institutions 6 (13): 37–53.
Guégan, D., and B. Hassani. 2013a. Multivariate vars for operational risk capital computation: A vine structure approach.International Journal of Risk Assessment and Management 17 (2): 148–170.
Guégan, D., and B. Hassani. 2013b. Using a time series approach to correct serial correlation in operational risk capital calculation.The Journal of Operational Risk 8 (3): 31–56.
Guégan, D., und B. Hassani. 2014. Distortion risk measure or the transformation of unimodal distributions into multimodal functions. In Future perspectives in risk models and finance, Alain Bensoussan, et al. (eds). Springer International Publisher, Switzerland.
Guégan, D., and P.-A. Maugis. 2010. Note on new prospects on vines.Insurance Markets and Companies: Analyses and Actuarial Computations 1 (1): 15–22.
Guégan, D., and P.-A. Maugis. 2011. An econometric study for vine copulas.International Journal of Economics and Finance 2 (1): 2–14.
Hassani, B. K., and A. Renaudin. 2013. The cascade bayesian approach for a controlled integration of internal data, external data and scenarios. Working Paper, Université Paris 1, ISSN: 1955-611X (halshs-00795046-version 1).
Huggenberger, M., and T. Klett. 2009. A g-and-h copula approach to risk measurement in multivariate financial models. Preprint, University of Mannheim, Germany.
Joe, H. 1997a.Multivariate models and dependence concepts (Monographs on statistics and applied probability). London: Chapman and Hall.
Joe, H. 1997b.Multivariate models and dependence concepts (Monographs on statistics and applied probability). London: Chapman and Hall.
Joe, H. 2005. Asymptotic efficiency of the two-stage estimation method for copula-based models.Journal of Multivariate Analysis 94:401–419.
Koehler, K. and J. Symanowski. 1995. Constructing multivariate distributions with specific marginal distributions.Journal Multivariate Anaysis 55 (2): 261–282.
Leadbetter, M. 1983. Extreme and local dependence in stationary sequences.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 65 (2): 291–306.
Lorenz, E. N. 2010. Deterministic nonperiodic flow.Journal of the Atmospheric Sciences 20 (2): 130–141.
Majnoni, G., M. S. Martinez-Peria, W. Blaschke, and M. T. Jones. 2001. Stress testing of financial systems: An overview of issues, methodologies and fsap experiences. Working paper, IMF.
McCulloch, J. 1996. On the parametrization of the afocal stable distributions.Bulletin of the London Mathematical Society 28:651–655.
Mendes, B., E. de Melo and R. Nelsen. 2007. Robust fits for copula models.Communications in Statistics-Simulation and Computation 36(5).
Merton, R. C. 1972. On the pricing of corporate debt: The risk structure of interest rates.Journal of Finance 29:449–470.
Pearson, K. 1900. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.Philosophical Magazine Series 5 50 (302): 157–175.
Pesola, J. 2007. Financial fragility, macroeconomic shocks and banks’ loan losses: evidence from europe. Working Paper, Bank of Finland Research.
Quagliariello, M. 2009.Stress-testing the banking system: Methodologies and applications. London: Cambridge University Press.
Riskmetrics. 1993. Var. JP Morgan. Introduction to creditmetrics. Technical Document.
Rockafellar, R., and S. Uryasev. 2000. Optimization of conditional value-at-risk.Journal of Risk 2 (3): 21–41.
Rockafellar, R., and S. Uryasev. 2002. Conditional value at risk for general loss distributions.Journal of Banking and Finance 26 (7): 1443–1471.
Rodriguez, J.-C. 2007. Measuring financial contagion: A copula approach.Journal of Empirical Finance 14:401–423.
Said, S. and D. Dickey. 1984. Testing for unit roots in autoregressive moving average models of unknown order.Biometrika 71 (3): 599–607.
Sereda, E., E. Bronshtein, S. Rachev, F. Fabozzi, W. Sun, and S. Stoyanov. 2010.Distortion risk measures in portfolio optimisation, volume 3 of Business and Economics. Springer US.
Siddique, A. and I. Hasan. 2013.Stress testing: Approaches, methods and applications. London: Risk Books.
Silverman, B. W. 1986.Density Estimation for statistics and data analysis. London: Chapman and Hall.
Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges.Publications De, l’Institut de Statistique de Paris 8:229–231.
Taleb, N. 2010.The Black Swan: the impact of highly improbable. 2nd ed. New York: Random House.
Taqqu, M., and G. Samorodnisky. 1994.Stable non-Gaussian random processes. New York: Chapman and Hall.
Wang, S. S. 2000. A class of distortion operators for pricing financial and insurance risks.Journal of Risk and Insurance 67 (1): 15–36.
Weiss, G. 2010. Copula parameter estimation-numerical considerations and implications for risk management.Journal of Risk 13 (1): 17–53.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Guégan, D., Hassani, B. (2015). Stress Testing Engineering: The Real Risk Measurement?. In: Bensoussan, A., Guegan, D., Tapiero, C. (eds) Future Perspectives in Risk Models and Finance. International Series in Operations Research & Management Science, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-07524-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-07524-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07523-5
Online ISBN: 978-3-319-07524-2
eBook Packages: Business and EconomicsBusiness and Management (R0)