Speaker: Professor Marie Kratz
Affiliation: ESSEC Business School Paris, CREAR Risk Research Center


There is an accepted idea that risk measurements are pro-cyclical: in times of crisis, they overestimate the future risk, while they underestimate it in quiet times. We lay down a simple and efficient methodology to evaluate the amount of pro-cyclicality in the way financial institutions measure risk. To do so, we introduce a new indicator based on the Sample Quantile Process (a dynamic extension of Value-at-Risk), conditioned on realized volatility. Using this framework, we prove that pro-cyclicality is inherent in risk measure estimates based on historical data. We identify two main factors explaining this pro-cyclical behavior: the clustering and return-to-the-mean of volatility, as it could have been anticipated but not yet quantified, and, more surprisingly, the very way risk is measured, even in a world with constant volatility, though the empirical magnitude of the mean-reversion is greater than what would be observed in that special case. We develop CLTs and FCLT’s for functionals of quantile and dispersion estimators to support theoretically those empirical findings. This is a joint work with Dr. Marcel Bräutigam and Dr. Michel Dacorogna.

About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics. 

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

  • computer 
  • data projector
  • chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.


Priestley Building (67)
442 (and via Zoom: https://uqz.zoom.us/j/81688396546)