Abstract
In this paper, we study a credit risk (collateral) management scheme for the Canadian retail payment system designed to cover the exposure of a defaulting member. We estimate ex ante the size of a collateral pool large enough to cover exposure for a historical worst-case default scenario. The parameters of the distribution of the maxima are estimated using two main statistical approaches based on extreme value models: Block-Maxima for different window lengths (daily, weekly and monthly) and Peak-over-Threshold. Our statistical model implies that the largest daily net debit position across participants exceeds roughly $1.5 billion once a year. Despite relying on extreme-value theory, the out of sample forecasts may still underestimate an actual exposure given the absence of observed data on defaults and financial stress in Canada. Our results are informative for optimal collateral management and system design of pre-funded retail-payment schemes.
Acknowledgements:
The views expressed in this paper are those of the authors, and do not represent an official position of Payments Canada. We would like to thank Neville Arjani, Brendan Carley and Walter Engert for helpful comments as well as seminar participants at the 2017 Canadian Economics Association conference and the 2017 Canadian Stata Users Group meetings. Jacho-Chávez, Petrunia, and Voia thank Payments Canada for financial support to undertake this research.
References
Arjani, N. (2016), A Primer on Credit Risk in Payments Canadas Automated Clearing Settlement System (ACSS). Payments Canada Discussion paper No. 6.Search in Google Scholar
Bank for International Settlements (2011), Payment, clearing and settlement systems in the CPSS countries. Available at http://www.bis.org/cpmi/publ/d97.pdfSearch in Google Scholar
Bensalah, Y. (2000), Steps in Applying Extreme Value Theory to Finance: A Review. Bank of Canada Working Paper: 2000–20.Search in Google Scholar
Chan K.F., P. Gray (2016), Extreme Value Theory and Risk Management in Electricity Markets. Pp. 405–426 in: F. Longin (ed), Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications.John Wiley & Sons, Inc., Hoboken, New Jersey.10.1002/9781118650318.ch15Search in Google Scholar
Coles, S. (2001), An Introduction to Statistical Modeling of Extreme Values.Springer-Verlag, London.10.1007/978-1-4471-3675-0Search in Google Scholar
Cox, D.R, E.J. Snell (1968), A General Definition of Residuals. Journal of the Royal Statistical Society. Series B 30: 248–275.10.1111/j.2517-6161.1968.tb00724.xSearch in Google Scholar
Danielsson, J., C. Zhou (2016). Why is Risk So Hard to Measure? DNB Working Paper: 2016–494.10.2139/ssrn.2712238Search in Google Scholar
Galbraith, J., S, Zernov (2009). Extreme dependence in the NASDAQ and S & P 500 composite indexes. Applied Financial Economics 19: 1019–1028.10.1080/09603100802360032Search in Google Scholar
Galbraith, J.W., G. Tkacz (2013), Analyzing Economic Effects of September 11 and Other Extreme Events Using Debit and Payments System Data. Canadian Public Policy 39: 119–134.10.3138/CPP.39.1.119Search in Google Scholar
Giles, D.E., H. Feng, R. Godwin (2013), On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution. Communications in Statistics - Theory and Methods 42: 1934–1950.10.1080/03610926.2011.600506Search in Google Scholar
Gregory, J. (2015), Counterparty Credit Risk: The New Challenge for Global Financial Markets. The Wiley Finance Series, West Sussex.Search in Google Scholar
Hendricks, D. (1996), Evaluation of Value-at-Risk Models Using Historical Data. Economic Policy Review 2: 39–70.10.2139/ssrn.1028807Search in Google Scholar
Hull, John (2007), VAR versus Expected Shortfall, Risk.net article. Available at https://www.risk.net/risk-magazine/technical-paper/1506669/var-versus-expected-shortfall.Search in Google Scholar
Huynh, K.P., D.T. Jacho-Chávez, R.J. Petrunia M. Voia, (2011), Functional Principal Component Analysis of Density Families With Categorical and Continuous Data on Canadian Entrant Manufacturing Firms. Journal of the American Statistical Association 106: 858–878.10.1198/jasa.2011.ap10111Search in Google Scholar
Huynh, K.P., D.T. Jacho-Chávez, R.J. Petrunia, M. Voia, (2015). A Nonparametric Analysis of Firm Size, Leverage and Labour Productivity Distribution Dynamics. Empirical Economics 48: 337–360.10.1007/s00181-014-0807-9Search in Google Scholar
Longin, F. (2016), Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications. John Wiley and Sons, Inc, Hoboken, New Jersey.10.1002/9781118650318Search in Google Scholar
Manning M., E. Nier, J. Schanz (2009), The Economics of Large-value Payments and Settlement. Oxford University Press, Oxford.Search in Google Scholar
Olivares, A., M. Tompkins (2016), Clearing and Settlement Systems from Around the World: A Qualitative Analysis. Bank of Canada Staff Discussion Paper: 2016–14.Search in Google Scholar
Perez-Saiz, H., G. Xerri (2016), Credit Risk and Collateral Demand in a Retail Payment System. Bank of Canada Staff Discussion Paper: 2016–16.Search in Google Scholar
Article note
This article is part of the special issue “Big Data” published in the Journal of Economics and Statistics. Access to further articles of this special issue can be obtained at www.degruyter.com/journals/jbnst.
© 2018 Oldenbourg Wissenschaftsverlag GmbH, Published by De Gruyter Oldenbourg, Berlin/Boston
