Measuring market risk : from Value-at-Risk (VaR) to Expected Shortfall (ES). The troublesome question of ES backtesting.

Abstract

Financial institutions rely on forecasts of risk measures for the purposes of internal risk man- agement as well as regulatory capital calculations. In this context, an important part in esti- mating risk is to evaluate how accurate the forecasts have been. This procedure is generally called backtesting. The Basel III Accord, is an internationally agreed set of recommendations developed by the Basel Committee on Banking Supervision (BCBS) in response to the global financial crisis of 2008. In this regulatory framework, a financial institution that intends to use an internal models approach (IMA) must conduct, amongst other requirements, some backtesting. As a key element of the post-crisis evolving regulatory framework, new standards for the mini- mum capital requirements against market risk exposures, adopted in 2016 and revised in 2019, introduce a shift from a Value-at-Risk (VaR) risk measure to an Expected Shortfall (ES) risk measurement approach. While the move from the VaR to the ES allows to tackle some deficiencies of the VaR, such as the coherence property and the ability to look at the tail-risk of the loss distribution, the shift from a quantile-based risk measure to a tail risk measure raises a number of theoretical questions, such as the effectiveness of backtesting; in particular it brings some new challenges regarding the backtesting of the ES models. This in-hand work starts by providing the needed theoretical background as well as a state-of- the-art of the ES backtesting methodologies proposed in the scientific literature to set up the foundations. Then, it aims at identifying a suitable ES backtesting framework - both mathemat- ically consistent and practically implementable - that a financial institution could implement in the near-future in the use of the new models based approach, meanwhile considering the associated revised regulatory requirements. Finally, an empirical research study is proposed in order to state on the relevance of the identified ES backtesting framework, but also more fundamentally on the pertinence of the new risk measurement approach in itself.