The Basel Accords require banks to set aside capital in line with their levels of risk. Currently, Value-at-Risk (VaR) is the applied risk measure of the potential loss in the value of a portfolio. In particular, 99% VaR isutilized, which is the loss that is likely to be exceeded only 1% of the time. While VaR is widely used and easy to compute, it has no information on the magnitude of the biggest 1% of losses. Moreover, it is not a coherent risk measure. Indeed, it is not subadditive, which means that VaR of a portfolio canbe higher than the sum of the VaRs of the individual assets in the portfolio. The Fundamental Review of the Trading Book is expected to make a complete revision of the approach to calculating risk-based capital requirements for investments. The 99% VaR is supposed to be replaced by 97.5% Expected Shortfall, which is the average of VaR(x) for x between 0.975 and 1. Li and Wang [2] studied the effect of this proposed change. Similarly to their work, we are examining higher-order Expected Shortfalls as potential alternative risk measures. The n-th-order Expected Shortfall is similar to the classical one (whichis a special case for n=1), the difference is that instead of a simple average, it is a weighted average of the VaR values, weighted by a function that dependson n. We define PELVE(n), which basically tells us what level n-th-order Expected Shortfall corresponds to a certain level VaR. In this talk we discuss some (online) approaches to handle the above mentioned risk measures: how to estimate them and detect changes.

[1] Barczy, M., K. Nedényi, F. and Sütő, L. (2023). Probability equivalent level of Value at Risk and higher-order Expected Shortfalls. Insurance: Mathematics and Economics 108, 107-128. ArXiv: https://arxiv.org/abs/2202.09770

[2] Li, H. and Wang, R. (2023). PELVE: Probability Equivalent Level of VaR and ES. Journal of Econometrics 234(1) 353-370. Available also at SSRN. 30(2) 325-341. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3489566