The Annals of Applied Statistics

Elicitability and backtesting: Perspectives for banking regulation

Natalia Nolde and Johanna F. Ziegel

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Conditional forecasts of risk measures play an important role in internal risk management of financial institutions as well as in regulatory capital calculations. In order to assess forecasting performance of a risk measurement procedure, risk measure forecasts are compared to the realized financial losses over a period of time and a statistical test of correctness of the procedure is conducted. This process is known as backtesting. Such traditional backtests are concerned with assessing some optimality property of a set of risk measure estimates. However, they are not suited to compare different risk estimation procedures. We investigate the proposal of comparative backtests, which are better suited for method comparisons on the basis of forecasting accuracy, but necessitate an elicitable risk measure. We argue that supplementing traditional backtests with comparative backtests will enhance the existing trading book regulatory framework for banks by providing the correct incentive for accuracy of risk measure forecasts. In addition, the comparative backtesting framework could be used by banks internally as well as by researchers to guide selection of forecasting methods. The discussion focuses on three risk measures, Value at Risk, expected shortfall and expectiles, and is supported by a simulation study and data analysis.

Article information

Ann. Appl. Stat., Volume 11, Number 4 (2017), 1833-1874.

Received: May 2016
Revised: March 2017
First available in Project Euclid: 28 December 2017

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Forecasting backtesting elicitability risk measurement procedure Value at Risk expected shortfall expectiles


Nolde, Natalia; Ziegel, Johanna F. Elicitability and backtesting: Perspectives for banking regulation. Ann. Appl. Stat. 11 (2017), no. 4, 1833--1874. doi:10.1214/17-AOAS1041.

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Supplemental materials

  • Supplementary material for article “Elicitability and backtesting: Perspectives for banking regulation”. We elaborate on some of the points made in the main article as well as provide technical details and proofs of several results.