Approaches and Techniques to Validate Internal Model Results

Dacorogna, Michel M (2017): Approaches and Techniques to Validate Internal Model Results.

Abstract

The development of risk model for managing portfolio of financial institutions and insurance companies require both from the regulatory and management points of view a strong validation of the quality of the results provided by internal risk models. In Solvency II for instance, regulators ask for independent validation reports from companies who apply for the approval of their internal models.

Unfortunately, the usual statistical techniques do not work for the validation of risk models as we lack enough data to significantly test the results of the models. We will certainly never have enough data to statistically estimate the significance of the VaR at a probability of 1 over 200 years, which is the risk measure required by Solvency II. Instead, we need to develop various strategies to test the reasonableness of the model.

In this paper, we review various ways, management and regulators can gain confidence in the quality of models. It all starts by ensuring a good calibration of the risk models and the dependencies between the various risk drivers. Then applying stress tests to the model and various empirical analysis, in particular the probability integral transform, we build a full and credible framework to validate risk models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Risk Models, validation, stress tests, statistical tests, solvency
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C49 - Other; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C59 - Other; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools

References

[1] P. Arbenz, D. Canestraro, 2012, Estimating Copulas for Insurance from Scarce Observations, Expert Opinion and Prior Information: A Bayesian Approach, Astin Bulletin, vol. 42(1), pages 271-290.

[2] P. Blum, 2004, On some mathematical aspects of dynamic financial analysis, ETH PhD Thesis, pages 1183.

[3] R. Bürgi, M. M. Dacorogna and R. Iles, 2008, Risk Aggregation, dependence structure and diversification benefit. chap. 12, pages 265-306, in \Stress testing for financial institutions", edited by Daniel Rösch and Harald Scheule, Riskbooks, Incisive Media, London.

[4] M. Busse, U. A. Müller, M. M. Dacorogna, 2010, Robust estimation of reserve risk, Astin Bulletin, vol. 40(2), pages 453-489.

[5] M. M. Dacorogna, 2015, A change of paradigm for the insurance industry, SCOR Papers, available under https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2730531.

[6] M. M. Dacorogna, L. El Bahtouri, M. Kratz, 2016, Explicit diversification benefit for dependent risks, SCOR Paper no. 38, available under http://www.scor.com/en/sgrc/ scor-publications/scor-papers.html.

[7] M. M. Dacorogna, A. Ferriero, D. Krief, 2015, Taking the one-year change from another angle, submitted for publication, available under https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2799286.

[8] M. M. Dacorogna, U. A. Müller, O. V. Pictet, C. G. De Vries, 2001, Extremal forex returns in extremely large data sets, Extremes, vol. 4(2) pages 105-127.

[9] F. X. Diebold, T. Gunther, A. Tay, 1998,Evaluating density forecasts with applications to financial risk management, International Economic Review, 39(4), pages 863-883.

[10] F. X. Diebold, J. Han, A. Tay, 1999,Multivariate density forecast evaluation and calibration in financial risk management: high-frequency returns on foreign exchange, Review of Economics and Statistics, vol. 81, page 661-673.

[11] A. Ferriero, 2016, Solvency capital estimation, reserving cycle and ultimate risk, Insurance: Mathematics and Economics, vol. 68, pages 162-168.

[12] T. Mack, 1993, Distribution-free calculation of the standard error of chain ladder reserve estimates Astin Bulletin, vol. 23(2), pages 213-255.

[13] M. Merz, M. V. Wüthrich, 2008, Stochastic Claims Reserving Methods in Insurance, Wiley Finance, John Wiley & Sons, Ltd, Chichester.