# Videos & Tutorials

See it with your own eyes- Fundamentals of approximation theory
- The power of the Chebyshev techniques; the maths behind them
- How our software library works
- Applications of the Chebyshev framework to enhance risk calculations

# Introductions…

#### Who we are and about this video series

3 minutes

#### The Computational Challenge

19 minutes

# Practical applications of our technology

#### Presentation at Bank of America

We were invited by Bank of America in London to present our research around risk calculation optimisation via Chebyshev and Machine Learning methods.

#### Vitamin B, Chebyshev, Homocysteine and... Dynamic Initial Margin

Chebyshev provides the tools for an accurate and ultra-fast stochastic simulation of dynamic sensitivities and Initial Margin. Find out how in this video

30 minutes

#### Chebyshev for IMA-FRTB

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 video is similar to the one titled “Machine Learning + Chebyshev for Risk calculations”, but making more emphasis on the IMA-FRTB results at at a Tier-1 bank.

#### Chebyshev Tensors & Machine Learning in Dynamic Initial Margin

In this presentation we see how Chebyshev Tensors and Machine Learning techniques can be used in the calculation of Dynamic Initial Margin (DIM). We start by giving an overview of the main mathematical properties behind Chebyshev Tensors. Then we see how these can be used to approximate pricing functions within risk calculations to alleviate the huge computational burden associated with them. Finally we explain how Chebyshev Tensors can be used in the calculation of DIM and present DIM calculations obtained with Chebyshev Tensors, Deep Neural Networks and other regression types.

# Our software library

#### Machine Learning + Chebyshev for Risk calculations

We describe how to use Chebyshev Tensors in combination with Machine Learning techniques to compute risk calculations efficiently.

This video is similar to the one titled “Computational Challenge of IMA FRTB”, but making more emphasis on the Machine Learning part of the algorithms.

#### Downloading the library

2 minutes

#### Installing the library

7 minutes

#### Documentation

4 minutes

#### Main functionality

**We strongly suggest you watch this video**

16 minutes

#### Function Derivatives

9 minutes

#### Serialization

4 minutes

#### Algebra of MoCaX Objects

7 minutes

#### Singularity Points & Splines

14 minutes

#### Slicing MoCaX Objects

5 minutes

#### Extrusion

5 minutes

#### Higher dimensions

24 minutes

#### Sliding

13 minutes

# Maths and Methods – fundamentals

#### Fundamentals of Approximation Theory and of the Chebyshev Methods - Part I

20 minutes

#### Fundamentals of Approximation Theory and of the Chebyshev Methods - Part II

24 minutes

#### Evaluation of Chebyshev Objects - the Barycentric Interpolation formula

15 minutes

#### Stability of the Barycentric Interpolation formula

Learn about the numerical stability of the Barycentric Interpolation formula

8 minutes

#### The Clenshaw algorithm

Here we explain the connection between the Clenshaw algorithm and the Barycentric Interpolation formula

4 minutes

# Maths and Methods – more advanced stuff

#### Accuracy & Error prediction

21 minutes

#### Singularity points & Splines (method)

7 minutes

#### Function Derivatives

17 minutes

#### High Dimensional Chebyshevs

27 minutes

#### Algebra of Chebyshev Objects

23 minutes