 Measuring Tail RisksKan Chen and Tuoyuan Cheng Abstract: Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk events (MPMR) that can occur over a length of time. MPMR underscores the dependence of the tail risk on the risk management time frame. Unlike VaR and ES, MPMR does not require specifying a confidence level. We derive the risk measure analytically for several well-known distributions. In particular, for the case where the size of the risk event follows a power law or Pareto distribution, we show that MPMR also scales with the number of observations $n$ (or equivalently the length of the time interval) by a power law, $\text{MPMR}(n) \propto n^{\eta}$, where $\eta$ is the scaling exponent. The scale invariance allows for reasonable estimations of long-term risks based on the extrapolation of more reliable estimations of short-term risks. The scaling relationship also gives rise to a robust and low-bias estimator of the tail index (TI) $\xi$ of the size distribution, $\xi = 1/\eta$. We demonstrate the use of this risk measure for describing the tail risks in financial markets as well as the risks associated with natural hazards (earthquakes, tsunamis, and excessive rainfall). Date: 2022-09, Revised 2022-11 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2209.07092 Access Statistics for this paper More papers in Papers from arXiv.org |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.