Topics on the Fundamental Review of the Trading Book

The Basel Committee on Banking Supervision has introduced a revised market risk framework and banks are expected to adopt the new rules by January 2023. This work addresses two of the major amendments to the framework: the capital calculation formula and the model validation standards for the internal model approach. The capital calculation formula has changed fundamentally and now relies on the expected shortfall measure and takes into account liquidity risk. We explain the details and state the mathematical foundations of the new formula for capital calculation and extend it to elliptical distributions. We demonstrate that in this case the formula gives an upper bound which can be explained by the aggregation across time taking place in the formula. The model validation regime for internal models now requires that models perform satisfactorily at trading desk level and for a range of quantiles in the tails of the loss distributions. To this end, we develop multi-desk backtests, which simultaneously backtest all trading desk models and which exploit all the information available in the presence of correlation between desks. We first consider tests based on indicator time series for VaR violations before proposing a multi-desk extension of the mono-desk spectral test of Gordy and McNeil (2020) which allow the evaluation of a model at more than one confidence level. The spectral tests make use of realised probability integral transform values based on the estimated loss distribution and these contain more information than the VaR violation indicators. A further proposed test extends Cochran Q-test to obtain a test that VaR violation rates across desks are equal as well as consistent with the targeted exception rate. The new backtests are easy to implement with reasonable running time. In extensive simulation studies, we compare the performance of the tests in terms of size and power.