A new approach to assessing model risk in high dimensions |
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| Institution: | 1. Grenoble Ecole de Management, Department of Finance, 12 rue Pierre Sémard, 38003 Grenoble cedex 01, France;2. Department of Economics and Political Science at Vrije Universiteit Brussel (VUB), Belgium;1. Cranfield School of Management, Cranfield University, Cranfield MK43 0AL, UK;2. The Sir John Cass Business School, City University, London, UK;3. Surrey Business School, University of Surrey, Guildford GU2 7XH, UK;1. Department of Accounting and Finance, University of Bristol, 8 Woodland Road, Bristol BS8 1TN, UK;2. Xfi Centre for Finance and Investment, University of Exeter, Streatham Court, Rennes Drive, Exeter EX4 4ST, UK;3. Essex Business School, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK;1. Department of Business Administration, Universidad Carlos III, Spain;2. D.G.A. Supervisión – Banco de España, Spain;1. School of Management, Zhejiang University, Hangzhou, Zhejiang 310058, PR China;2. Department of Management Studies, College of Business, University of Michigan – Dearborn, 19000 Hubbard Drive, Dearborn, Michigan 48126-2638, USA;1. Freie Universität Berlin, Department of Economics, D-14195 Berlin, Germany;2. University of Regensburg, Department of Economics and Econometrics, D-93040 Regensburg, Germany;3. Institute for Employment Research (IAB), Germany;4. IOS Regensburg, Germany;1. Tasmanian School of Business and Economics, University of Tasmania, Hobart, TAS 7001, Australia;2. Department of Economics, Macquarie University, Balaclava Road, North Ryde, NSW 2109, Australia;3. Discipline of Finance, The University of Sydney Business School, University of Sydney, NSW 2006, Australia;4. School of Economics, University of New South Wales, NSW 2052, Australia |
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| Abstract: | A central problem for regulators and risk managers concerns the risk assessment of an aggregate portfolio defined as the sum of d individual dependent risks . This problem is mainly a numerical issue once the joint distribution of is fully specified. Unfortunately, while the marginal distributions of the risks are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any risk assessment of the portfolio is subject to model uncertainty.Previous academic research has focused on the maximum and minimum possible values of a given risk measure of the portfolio when only the marginal distributions are known. This approach leads to wide bounds, as all information on the dependence is ignored. In this paper, we integrate, in a natural way, available information on the multivariate dependence. We make use of the Rearrangement Algorithm (RA) of Embrechts et al. (2013) to provide bounds for the risk measure at hand. We observe that incorporating the information of a well-fitted multivariate model may, or may not, lead to much tighter bounds, a feature that also depends on the risk measure used. In particular, the risk of underestimating the Value-at-Risk at a very high confidence level (as used in Basel II) is typically significant, even if one knows the multivariate distribution almost completely.Our results make it possible to determine which risk measures can benefit from adding dependence information (i.e., leading to narrower bounds when used to assess portfolio risk) and, hence, to identify those situations for which it would be meaningful to develop accurate multivariate models. |
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| Keywords: | Model risk VaR Rearrangement Algorithm Tail dependence Outlier detection Minimum variance portfolio Credit risk management |
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