The calculation of capital within the Fundamental Review of the Trading Book regulation (FRTB) requires, under Internal Models Approach (IMA), the daily calculation of expected shortfalls (ES) with different liquidity horizons. The calculation of ES requires the pricing of portfolios on hundreds if not thousands of scenarios. This means each trade needs to be priced daily, depending on the different liquidity horizons, between 250 and a few thousand scenarios.
On top of this daily calculation, there is a period of stress that must be estimated at least quarterly, which involves the valuation, of each trade, on around 3000 scenarios (around 10 years of historical data). Although the latter must be done quarterly, there is heavy pressure from regulators to do it monthly. The PLA test, which compares daily risk-theoretical P&L with the daily Hypothetical P&L for each trading desk, has forced banks to price their portfolios for the calculation of ES with front office systems. This considerably increases the operational and computational burden on banks forcing them to look for ways to reduce these costs.
In this paper, researchers Mariano Zenon and Ignacio Ruiz introduce a new technique based on high‐dimensional Chebyshev Tensors that they call “orthogonal Chebyshev sliding technique”. They implemented this technique inside the systems of a tier one bank, and used it to approximate front office pricing functions in order to reduce the substantial computational burden associated with the capital calculation as specified by FRTB IMA.
In all cases, the computational burden reductions obtained were 90+%, while keeping high degrees of accuracy. The latter obtained as a result of the mathematical properties enjoyed by Chebyshev tensors. The work will be presented in a webinar in April hosted by GARP’s London chapter.