Measuring tail risks

نویسندگان

چکیده

Value at risk (VaR) and expected shortfall (ES) are common high quantile-based measures adopted in financial regulations management. In this paper, we propose a tail measure based on the most probable maximum size of events (MPMR) that can occur over length time. MPMR underscores dependence management time frame. Unlike VaR ES, does not require specifying confidence level. We derive analytically for several well-known distributions. particular, case where event follows power law or Pareto distribution, show also scales with number observations $n$ (or equivalently interval) by law, $\text{MPMR}(n) \propto n^{\eta}$, $\eta$ is scaling exponent. The scale invariance allows reasonable estimations long-term risks extrapolation more reliable short-term risks. relationship gives rise to robust low-bias estimator index (TI) $\xi$ $\xi = 1/\eta$. demonstrate use describing markets as well associated natural hazards (earthquakes, tsunamis, excessive rainfall).

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ژورنال

عنوان ژورنال: The Journal of Finance and Data Science

سال: 2022

ISSN: ['2405-9188']

DOI: https://doi.org/10.1016/j.jfds.2022.11.001