Backtesting Lambda Value at Risk

TL;DR

This paper introduces three nonparametric backtesting methods for the Lambda VaR, a generalized risk measure, and compares their effectiveness with existing approaches through empirical analysis.

Contribution

It proposes novel nonparametric backtesting procedures for Lambda VaR, including bilateral and distribution-dependent tests, enhancing validation methods for this new risk measure.

Findings

Two tests assess coverage correctness.

One test evaluates distribution-dependent accuracy.

Backtesting results compare favorably with existing methods.

Abstract

A new risk measure, the lambda value at risk (Lambda VaR), has been recently proposed from a theoretical point of view as a generalization of the value at risk (VaR). The Lambda VaR appears attractive for its potential ability to solve several problems of the VaR. In this paper we propose three nonparametric backtesting methodologies for the Lambda VaR which exploit different features. Two of these tests directly assess the correctness of the level of coverage predicted by the model. One of these tests is bilateral and provides an asymptotic result. A third test assess the accuracy of the Lambda VaR that depends on the choice of the P&L distribution. However, this test requires the storage of more information. Finally, we perform a backtesting exercise and we compare our results with the ones from Hitaj and Peri (2015)