On the properties of the Lambda value at risk: robustness, elicitability and consistency

TL;DR

This paper examines the Lambda value at risk (Lambda VaR), demonstrating that it possesses robustness, elicitability, and consistency, making it a promising risk measure for financial risk assessment.

Contribution

It establishes that Lambda VaR satisfies robustness, elicitability, and consistency properties, enhancing its credibility and utility in risk measurement.

Findings

Lambda VaR is robust to small data changes.

Lambda VaR is elicitable, enabling effective backtesting.

Lambda VaR satisfies the consistency property under certain conditions.

Abstract

Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable for assessing the accuracy of such an estimation and this can be naturally achieved by elicitable risk measures. For the same objective, an alternative approach has been introduced by Davis (2016) through the so-called consistency property. On the other hand, a risk estimation should be less sensitive with respect to small changes in the available data set and exhibit qualitative robustness. A new risk measure, the Lambda value at risk (Lambda VaR), has been recently proposed by Frittelli et al. (2014), as a generalization of VaR with the ability to discriminate the risk among P&L distributions with different tail behaviour. In this article, we show that Lambda VaR also satisfies the properties of robustness, elicitability and consistency under some conditions.