Machine Learning for Risk Calculations

We like the challenge of difficult calculations
Chebyshev Learning


  • Acceleration of Counterparty Credit Risk simulations – XVAs, PFE, IMM capital
  • Acceleration of ES calculation in  IMA FRTB
  • Reduction of computational cost in Risk Calculations
  • Simulation of sensitivities inside a Monte Carlo engine
  • Dynamic Initial Margin (DIM) simulation
  • Portfolio optimisation algorithms
  • Balance Sheet optimisation
  • Pricing function cloning from pricing libraries to separated risk engines


The solutions we have designed are grounded on a number of Machine Learing techniques, Deep Neural Nets and Chebyshev Tensors


There are a number of resources that we share so you can run your own research and investigate what you need

MoCaX Library

Our library is available for free download. Implement Chebyshev Learning with it

Who we are

We are a bunch of geeks that feel passionate about computational challenges

Contact us

We love hearing from other’s research, share ideas, answer questions

In this book, I. Ruiz and M. Zeron share the line of research they have taken for several years on the topic of optimising the computation of risk calculations.

Part I - Fundamental Approximation Methods

Chapter 1. Machine Learning
Chapter 2. Deep Neural Networks
Chapter 3. Chebyshev Tensors

Part II - The toolkit, plugging in approximation methods

Chapter 4. Introduction, why a toolkit is needed
Chapter 5. Composition techniques
Chapter 6. Tensors in TT format and tensor extension algorithms
Chapter 7. Sliding technique
Chapter 8. The Jacobian projection technique

Part III - Hybrid solutions, approximations methods and the toolkit

Chapter 9. Introduction to hybrid solutions
Chapter 10. The toolkit and Deep Neural Nets
Chapter 11. The toolkit and Chebyshev Tensors
Chapter 12. Hybrid Deep Neural Nets and Chebyshev Tensors frameworks

Part IV - Applications

Chapter 13. The aim
Chapter 14. When to use Deep Neural Networks and when to use Chebyshev Tensors
Chapter 15. Counterparty credit risk
Chapter 16. Market risk
Chapter 17. Dynamic sensitivities
Chapter 18. Pricing model calibration
Chapter 19. Approximation of the implied volatility function
Chapter 20. Optimisation problems
Chapter 21. Pricing cloning
Chapter 22. XVA sensitivities
Chapter 23. Sensitivities of exotic derivatives
Chapter 24. Software libraries relevant to the book