Backtesting expected shortfall: a duration-severity approach


10:00 AM - 11:00 AM



  • Time: 10:00-11:00 am   (Beijing Time)
  • Date: Monday, April 29, 2024
  • Venue: MB441
  • Speaker:Dr. Yang Lu, Concordia University
  • Host:Dr. Jiajun Liu


We propose an original two-part, duration-severity approach to backtesting expected shortfall. From the daily probability integral transform of the return, we construct a sequence of durations counting the time elapsed between successive VaR violations, as well as a sequence of severities corresponding to the realized quantiles in case of a violation. Then the serial and mutual independence of the duration and severity sequences are tested using the theory of (bivariate) orthogonal polynomials. Our test includes as special cases unconditional coverage (UC) and conditional coverage (CC) backtests of both VaR and ES, allowing the risk manager to easily identify the mis-specified component(s) of the internal model in case of a rejection of the test. Our test can also be applied to other systemic risk measures, such as the marginal expected shortfall. Simulation experiments suggest that our test has good finite sample properties for realistic sample sizes. A case study illustrates the usefulness of the proposed test. This is a joint work with Christophe Hurlin (University of Orleans, France) and Sullivan Hue (Aix-Marseille University, France).


Yang Lu is assistant professor (and associate professor as of June 2024) at Concordia University in Montreal, Canada. He previously worked as assistant professor at University of Paris 13 from 2017 to 2020, as a postdoc total fellow from 2015 to 2017 at Aix-Marseille University. He studied maths at École Normale Supérieure, Paris and actuarial science at Ecole Nationale de la Statistique et de l’administration économique (now IP Paris). He completed his PhD in applied mathematics at University of Paris Dauphine, under the supervision of Christian Gourieroux. His research interest is statistical and econometric methodology for insurance and finance applications. He has published 25 papers to date, in journals such as IME, JRI, Astin, SAJ, Management Science, Mathematical Finance, Journal of Banking and Finance, Electronic Journal of Statistics, Scandinavian Journal of Statistics, Journal of Multivariate Analysis, JRSSA, Journal of Time Series Analysis, and Journal of Applied Econometrics.

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