The FRTB Internal Model is an evolution of Value at Risk (Var) which has been the principal measure of market risk used by regulators since the mid 1990s. While the strengths of Var are desirable (an objective statistical and testable measure of risk which crosses market boundaries), issues with Var that the Basel committee have attempted to address are:
Non-normality - the tendency for extreme rate movements to occur more often than a simple measure of standard deviation would predict.
Cyclical risk - in quiet times, the volatility of rates can fall, giving a false sense of security about the potential for large losses.
Liquidity - Var does not take into account the extra risk from being forced to hold illiqid positions, particularly in extreme market conditions.
The committee has addressed these specific concerns by proposing the following features in the new internal model:
The new model favours using expected shortfall (the average loss from all observations in the tail of the distribution). In conjunction with historic simulation, which imposes no normal assumption, the result is seen to be more representative of actual losses from extreme market moves.
To avoid cyclical risk a historic simulation over a 1 year period of high volatility is the basis for the model. To the bystander this would be the GFC but depending on the institutions portfolio mix it could be another period, hence calibration is required to find the most volatile period. This creates an issue with sourcing rate history. In some cases history is unavailable or inappropriate so the historic stress simulation does not incorporate all risk factors. The answer to this is to run two further simulations over the most recent year of history; one simulation with all risk factors and another with the reduced set matching the stress simulation. The ratio of these two results provides a scaling factor.
Instruments are given a liquidity value according to research done by the Basel committee. The internal model needs to incorporate these values by either applying rate shifts from historic intervals greater than one day, or by scaling up historic one day intervals by the square root of the liquidity value. Both of these techniques have theoretical implications for the testability of the model (a strength of Var was its straightforward back testing methodology) however the benefit of a more realistic risk measure is seen to outweigh the concern of a more complicated back testing methodology.
Calculation
The foundation component of the Vector Risk IMA calculation is historic simulation. in the software, this process is identical to Historic Var except that the expected shortfall (ES) statistic is extracted from all results in the tail of the sorted scenario Mtms, whereas in Var we would just take the observation at the confidence interval.
The steps therefore to running IMA are as follows:
(Note: A desk is defined in the business unit hierarchy as the aggregation of one or more trading books.)
At the desk level:
Call the MarketInternal analytic in the risk engine, supplying all of the trade references belonging to that desk.
The MarketInternal calculation will run 15 sub-calculations. Each of these calculations is a historic simulation for one of three combinations of historic scenario (full factor, current period, reduced factor current period, reduced factor stress period) and one of five liquidity settings (10,20,40,60,120), where the latter simulations only shift more illiquid curves.
Each historic simulation manages a further subdivision to calculate six ES results, one for each of the markets (GIRR, CSR, Equity, Commodity, FX) and a total ES.
So now we have 90 ES results for the desk.
Portfolio Mtms on each scenario underlying the calculation of each of these 90 ES results are stored in the Results database.
At the global level:
Call the AggregateMarketInternal analytic in the risk engine, supplying the list of calculation GUIDs from all of the desk level calculations.
The AggregateMarketInternal analytic sums the portfolio Mtms that were stored in the desk level calculations on a like for like basis (ie all of the desks had a scenario Mtm for ES 37 and historic scenario 125, so the global Mtm for 37,125 is the sum of all the desk ones).
The global level scenarios for each of the 90 calculations are re-sorted and a global ES result for each is obtained.
The regulatory formula is used to combine the 90 ES results into the risk weighted assets result IMCC(C).
The calculations can be run directly in the risk engine, however the Vector Risk workflow supports a typical bank calculation by co-ordinating the desk level calls to the risk engine, making the aggregation calls with the correct calculation GUIDs, and finally showing summary and detail reports.
Reference
For the full FRTB specification from Basel please refer to the following document:
www.bis.org/bcbs/publ/d352.pdf