Modeling Expected Shortfall Using Tail Entropy

Abstract

Given the recent replacement of value-at-risk as the regulatory standard measure of risk with expected shortfall (ES) undertaken by the Basel Committee on Banking Supervision, it is imperative that ES gives correct estimates for the value of expected levels of losses in crisis situations. However, the measurement of ES is affected by a lack of observations in the tail of the distribution. While kernel-based smoothing techniques can be used to partially circumvent this problem, in this paper we propose a simple nonparametric tail measure of risk based on information entropy and compare its backtesting performance with that of other standard ES models.

Local Intrinsic Dimensionality, Entropy and Statistical Divergences

“…Inclusion of the extra q parameter can assist with higher robustness to anomalies and better fitting to characteristics of data distributions. Tail entropy has been used in financial applications for measuring the expected shortfall [ 61 ] in the upper tail using quantization. This is different from our context, where the our exclusive focus is on lower tails and we develop exact results for an asymptotic regime where lower tail size approaches zero.…”

Econophysics of cryptocurrency crashes: an overview

“…Pele [135] investigated the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using highfrequency data for Bitcoin, they estimated the entropy of the intraday distribution of log-returns through the symbolic time series analysis STSA, producing low-resolution data from high-resolution data.…”