Deficiencies of the Basel III standard approach for CVA capital charge led to fundamental changes in the proposed Fundamental Review of the Trading Book FRTB SA-CVA framework. With this approach, banks have to compute CVA sensitivities to a large number of market risk factors, which are typically in the hundreds or even thousands. The FRTB-CVA document states: “CVA sensitivities to market risk factors are computationally very expensive.” (While this is true for the traditional bump-and-revalue approach (finite differences) as it means hundreds to thousands of revaluations of the entire CVA multi-step Monte-Carlo simulation, Adjoint Algorithmic Differentiation (AAD) provides a way out. With AAD, all sensitivities can be obtained at a small additional computational cost compared to a single valuation.

This paper gives a brief overview of the proposed FRTB SA-CVA framework, discusses the complexities and reviews approaches for computing CVA sensitivities. It shows how AAD can be applied leading to large performance gains and gives practical implementation guidelines.

  • FRTB SA-CVA overview (CVA Capital – BCBS 265)
  • Computing CVA sensitivities
  • Challenges of the multi-step Monte-Carlo
  • Developing clean maintainable AAD code
  • AAD manual implementation and automatic tools
  • Incorporating external libraries
  • Combining AAD and bumping
  • Lowering the memory footprint