Juan Juan Cai & Anja Jansen


At Erasmus Universiteit Rotterdam (March 28, 2024)

11:00-11:45 Juan Juan Cai (Vrije Universiteit Amsterdam)

Title: Risk of Extreme Accounting Failures

Abstract: We use extreme value theory to estimate the risk of extreme accounting failures using U.S. restatement data over the period 1995-2022. This risk has as yet rarely been quantified, even though its reduction is a commonly cited policy objective in  financial reporting regulation. Although we find that the Value-at-Risk has been halved after the introduction of the Sarbanes-Oxley act, extreme financial restatement risk on the U.S. stock market remains substantial: the estimated 1-year probability of a more than $1bn downward correction in net income is still close to 40%.

This is a joint work with Kees Camfferman, Andre Lucas and Jacco L. Wielhouwer

Lunch Break

12:00-13:00 Anja Jansen (Otto-von-Guericke-Universität Magdeburg)

Title: Metric embeddings of tail correlation matrices


The assessment of risks associated with multivariate random vectors relies heavily on understanding their extremal dependence, crucial in evaluating risk measures for financial or insurance portfolios. A widely-used metric for assessing tail risk is the tail correlation matrix of tail correlation coefficients. Among the exploration of structural properties of the tail correlation matrix the so-called realization problem of deciding whether a given matrix is the tail correlation matrix of some underlying random vector has recently received some attention.

The entries of the tail correlation matrix are closely related to a useful distance measure on the space of Frechet-random variables, named spectral distance and first introduced in Davis & Resnick (1993). We analyze the properties of a related semimetric and show that it has the special property of being embeddable both in vector and function space, equipped with the respective sum norm. Notably, these embeddings bear a direct relationship with the realization of specific tail dependence structures via max-stable random vectors. Particularly, an embedding in vector space, employing so-called line metrics, provides a representation through a max-stable mixture of so-called Tawn-Molchanov models, s. also Fiebig, Strokorb & Schlather (2017).

Leveraging this framework, we revisit the realization problem, affirming a conjecture by Shyamalkumar & Tao (2020) regarding its NP-completeness.

This talk is based on joint work with Sebastian Neblung (University of Hamburg) and Stilian Stoev (University of Michigan).