Regression Sensitivities for Initial Margin Calculations

Abstract

Implementations of the Standard Initial Margin Model (SIMM) and the Sensitivity Based Approach (SBA) in the Fundamental Review of the Trading Book (FRTB), both call for the calculation of sensitivities with respect to a standardised set of risk factors. Since standard factors are generally collinear and pricing functions are possibly rough, finding sensitivities qualifies as a mathematically ill-posed problem for which analytical derivatives do not provide a robust solution. Numerical instabilities are particularly problematic since they hamper reconciliation and make collateral optimisation strategies inefficient.In this article, we introduce a method for calculating sensitivities based on ridge regressions to keep sensitivities small and stable. We find that a drift term and FX cross-gammas significantly improves the accuracy of the P&L explain achieved in the SIMM methodology. The method implies rigorous upper bounds on errors in P&L explain, on which basis we adjust Initial Margin conservatively in order to pass back-testing benchmarks.