Modeling with scarce data: Credit and
Transcription
Modeling with scarce data: Credit and
Modeling with small data: Credit and Operational Risk 13th congrès des actuaires, Peter Middelkamp, Small Data Example 1: Operational Risk 13th congrès des actuaires | Peter Middelkamp | Small Data 2 Operational Risk1 : (typically) Available Data • Internal sources: 0.99 – Own loss history collected over the past 5-10 years 0.98 0.97 – Expert judgement of loss potentials – Industry loss data from loss data exchanges (eg: ORX) – Public information (eg: corporate filings, rating agencies, news, Algo First) 0.96 F(x) • External sources: Empirical CDF 1 0.95 0.94 0.93 0.92 model internal loss data external data 0.91 0.9 0 500 1000 x 1500 2000 13th congrès des actuaires | Peter Middelkamp | Small Data 3 severity distribution per scenario and legal entity • truncated Pareto with one important input: A = Anticipated Loss Potential for a given confidence level e.g. f = 99.5%. 13th congrès des actuaires | Peter Middelkamp | Small Data 4 aggregation with dependence • Dependence within operational risk: – Dependence between legal entities – Dependence between event categories • External dependencies: – Dependence to financial markets (more prevailing in banks) – Dependence to pandemic events 13th congrès des actuaires | Peter Middelkamp | Small Data 5 Conclusion Operational risk • All parameters are mainly based on expert judgement that might be inspired by historic events in the firm and that happened to peers. • A simple dependence method is a must (e.g. mixture of full dependence, independence) • Number of parameters should be kept at a minimum to have a stable, easy to understand "well behaved" model. • Continue to collect data and use it as benchmark for the model. • Model alternatives (rejected): – LDA (not enough data) – Standard Formula (based on industry averages) – causal models with explicit control modelling (complicated, potentially unstable) – combining loss data sources and expert judgement using Bayesian inference (potentially unstable) 13th congrès des actuaires | Peter Middelkamp | Small Data 6 Example 2: Credit Risk 13th congrès des actuaires | Peter Middelkamp | Small Data 7 Compared to operational risk, there is plenty of data AAA and BB history 1920-2013 • Default history exposes large spikes. 10 8 BB 6 AAA 4 2 0 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 • Rating information alone is not enough to determine default risk 12 Default rate [%] • Some rating categories never experienced a default within one year 14 13th congrès des actuaires | Peter Middelkamp | Small Data 8 Multi year default probabilities can be used to estimate one year default probabilities Cumulative default probability AAA rating Fit Data 10.000% 1.000% 0.100% 0.010% 0.001% 1 3 5 7 9 11 13 15 17 19 Years • Note that a minimum default probability of 0.03% is applied to corporates, 0.01% to sovereigns. 13th congrès des actuaires | Peter Middelkamp | Small Data 9 Modelled default probabilities should be able to reproduce and go beyond historic realisations • Credit portfolio risk models capture historic default history (back-test) DP 13th congrès des actuaires | Peter Middelkamp | Small Data 10 Credit portfolio risk models should also capture historic dependencies to financial markets (back-test) • Default rates are higher when equity markets are down/ credit spreads widen (not that there is sometimes the default rate lags behind financial markets) 13th congrès des actuaires | Peter Middelkamp | Small Data 11 13th congrès des actuaires | Peter Middelkamp | Small Data 12 Legal notice ©2014 Swiss Re. All rights reserved. You are not permitted to create any modifications or derivative works of this presentation or to use it for commercial or other public purposes without the prior written permission of Swiss Re. The information and opinions contained in the presentation are provided as at the date of the presentation and are subject to change without notice. Although the information used was taken from reliable sources, Swiss Re does not accept any responsibility for the accuracy or comprehensiveness of the details given. All liability for the accuracy and completeness thereof or for any damage or loss resulting from the use of the information contained in this presentation is expressly excluded. Under no circumstances shall Swiss Re or its Group companies be liable for any financial or consequential loss relating to this presentation. 13th congrès des actuaires | Peter Middelkamp | Small Data 13