The new borders of Regtech in FRTB

Adjoint Algorithmic Differentiation & Machine Learning


On January 14th 2016, the Basel Committee on Banking Supervision (BCBS) published its revised capital requirements for market risk. The final standard, also known as the Fundamental Review of the Trading Book (FRTB), is intended to harmonise the treatment of market risk across national jurisdictions and will generally result in higher global capital requirements for financial institutions, both with IMA and Standard Approach. Following this, banks have asked Avantage Reply to analyse the calculation of the capital requirements under the Standardised Approach.


Avantage Reply is assisting banking groups with the implementation of the new market risk capital framework using the following strategic approach:

  • Conducting an in-depth analysis of the new regulatory framework and defining the guidelines for its subsequent implementation;
  • Comparing the current P&L process to the P&L attribution process under FRTB, thereby defining the functional requirements for passing the Internal Model eligibility test at the trading desk level;
  • Mapping market risk factors (Equity Risk, General Interest Rate Risk – GIRR, Commodity, Forex Risk, Credit Spread Risk - CSR) for each trading desk;
  • Testing which risk factors are modellable;
  • Implementing a user friendly prototype to calculate the Delta, Vega, Curvature & Default Risk Charges, and the Risk Add-on under the SBA methodology.

In this respect, Avantage Reply is supporting companies in the definition of methodological and functional requirements necessary for the development of two numerical methodologies: Adjoint Algorithmic Differentiation and Machine Learning.

  • Adjoint Algorithmic Differentiation (AAD)

    Adjoint Algorithmic Differentiation (AAD) is an advanced numerical methodology for the calculation of sensitivities. Avantage Reply uses this technique in order to support the business in:

    • Calculating capital requirements for market risk management;

    • Calculating measures as required by the new regulations: FRTB – SA, SIMM, FRTB – CVA;

    • Supporting the front office through enhanced pre-deal analysis;

    • Actively managing regulatory capital (RWA).

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    AAD is a numerical technique popularised by prof. Luca Capriotti in his paper of 2012. It enables faster computation of sensitivities as compared with the traditional 'bump and re-price' approach. The use of AAD provides the ability to compute in near real time the sensitivities of NPV and XVA. This would not be possible with standard methods. Formally, the AAD consists of three main steps:

    • Splitting: the pricing or XVA function is decomposed in simpler pieces;

    • Forward Propagation: the function value is computed via intermediate steps;

    • Adjoint Differentiation: the computation of the gradient is performed going «backward».


    Machine learning uses artificial intelligence and deep learning to understand patterns in data sets as to parametrise models based on a given objective function.

    Avantage Reply implemented Reinforcement Learning to constrained optimization problems such as P&L maximization and capital minimization (as computed under the new Standardised Approach).