**Computational Challenge of IMA FRTB. Solutions via Chebyshev Tensors - Slides**

**In **this talk we present results obtained within the systems of a tier-1 bank for a capital calculation within FRTB IMA, using Chebyshev tensors to massively accelerate and economise the calculation while retaining a high level of accuracy required by the regulation. This capital calculation, requires the pricing of portfolios thousands of times, which comes at a huge computational and economic cost.

We first present the main mathematical properties of Chebyshev tensors. Then we focus on why they are such powerful pricing approximators and how they can be applied to different risk calculations. Finally, we discuss and analyse the results obtained in the context of FRTB in a tier-1 bank.

- Why are Chebyshev interpolants so powerful?
- Simplicity of implementation
- Exponential convergence of Chebyshev Spectral Decomposition techniques
- Fast stable evaluation

- How to use the power of Chebyshev spectral methods within real risk calculation engines
- The curse of dimensionality
- Solutions to it: sliding technique, composition technique and Completion-Machine Learning algorithm
- Which solution is best for each application

- PoC results within the FRTB IMA framework of a tier one bank
- Real results of PoC performed in a bank
- ES and capital calculation accuracy
- Stability of the technique(s)

- Options for free software available for inhouse testing and implementation

### Presenter: Mariano Zeron: Head of Research and Development: MoCaX Intelligence

Mariano leads our Research & Development work. He has vast experience in Chebyshev Spectral Decomposition, machine-learning and related disciplines, and their application to quantitative problems in the financial markets. Mariano holds a Ph.D. in Mathematics from Cambridge University.