Abstract
The Fundamental Review of the Trading Book is a market risk measurement and management regulation recently issued by the Basel Committee. This reform, often referred to as “Basel IV”, intends to strengthen the financial system. The newest capital standard relies on the use of the Expected Shortfall. This risk measure requires to get sufficient information in the tails to ensure its reliability, as this one has to be alimented by a sufficient quantity of relevant data (above the 97.5 percentile in the case of the regulation or interest). In this paper, after discussing the relevant features of Expected Shortfall for risk measurement purposes, we present and compare several methods allowing to ensure the reliability of the risk measure by generating information in the tails. We discuss these approaches with respect to their relevance considering the underlying situation when it comes to available data, allowing practitioners to select the most appropriate approach. We apply traditional statistical methodologies, for instance distribution fitting, kernel density estimation, Gaussian mixtures and conditional fitting by Expectation-Maximisation as well as AI related strategies, for instance a Synthetic Minority Over-sampling Technique implemented in a regression environment and Generative Adversarial Nets.
Highlights
The Fundamental Review of the Trading Book (FRTB) is a market risk measurement and management regulation recently issued by the Basel Committee
It is noteworthy to mention that though goodness-of-fit tests might be of interest, they are limited by the information contained in the data used; for example, the goodness-of-fit tests are only valid if the sample of data used covers the full range of potential values, which is rarely the case, and even so, it tends to be biased by the behaviour of the data which represent the body of the distribution when in our case distribution tails matter the most
If there are no data points beyond the VaR set as a threshold (97.5% in the case of the newest market risk capital standards), the expected shortfall (ES) will not be robust, and in the most extreme case, can be equal to the VaR itself
Summary
The Fundamental Review of the Trading Book (FRTB) is a market risk measurement and management regulation recently issued by the Basel Committee. One of the rules imposed by the Basel regulatory framework is that the capital charge pertaining to market risks is supposed to be calculated on a daily basis using VaR measurement and usually relying on an internal model This rule needs to develop methods to estimate the loss probability distribution function every day, in order to compute VaR and ES using (at least) a one-year data period, assuming, in practice, the stationarity of the loss distribution over time. This assumption has proved to be unrealistic, as financial assets properties and behaviours are generally not the same: for example, during stable periods and crisis, the results obtained during a turmoil using a model calibrated on data obtained during a stable period is unlikely to be useful. Academic interest for expectiles has more to do with (real or supposed) theoretical weaknesses in VaR and ES than with a huge interest across the industry and are related with the fact that expectiles are coherent measures of risk (see [12,13,14])
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