With the Fundamental Review of the Trading Book (FRTB, BCBS 265), the method to compute the market risk capital under the Basel III framework drastically changed. The standard method (SBA) now follows a sensitivity-based approach (SBA), i.e. it is based on portfolio sensitivities to the market risk factors – specifically delta, vega, and curvature risk. Delta and vega are defined as first order derivatives, which are to be computed with shift-and-revalue in the FRTB framework with prescribed shifts. This requires a full re-valuation of the Monte-Carlo simulation for every risk factor and is hence computationally inefficient. On the other hand, Adjoint Algorithmic Differentiation (AAD) allows to obtain all sensitivities in a single valuation, at a fixed computational cost.

This paper gives an overview of FRTB SBA, discusses its definition of the delta and vega sensitivities, and illustrates how AAD can be used to compute them. It further details how to compute incremental changes of the capital charge for pre-trade analysis with AAD. The paper gives examples and shows the performance and accuracy benefits.

  • FRTB SBA overview
  • AAD introduction and tools
  • Applicability of ADD for FRTB SBA delta and vega risk
  • Incremental pre-trade analysis with AAD
  • Developing user-friendly AAD code
  • Performance optimisation hints
  • Reducing the memory footprint
  • AAD vs. bumping through a practical example