Videos & Tutorials

See it with your own eyes

In this page, you will be able to access lots of videos & tutorials that we have prepared for you. They will help you better understand

  • 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


Who we are and about this video series

We introduce ourselves and explain what to expect from these videos

3 minutes

The Computational Challenge

We explain the computational challenge that financial institutions are facing and introduce the solution via Chebyshev Spectral Decomposition

19 minutes

Practical applications of our technology

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

CVA and IMM for exotics and large portfolios

Computing CVA and/or IMM capital for exotic products is computationally challenging. It can also be difficult for large portfolios of vanilla products. In this video, we see how Chebyshev methods can increase the performance of existing Monte Carlo engines by orders of magnitude, facilitating the fast and efficient computation of CVA and IMM numbers for exotics and large portfolios


The computational requirements of brute-force IMA-FRTB are outstanding. Here we see how they can be reduced to 1/10th with Chebyshev Spectral Decompositions methods

Our software library

Downloading the library

Here you see how easy it is to download the MoCaX library

2 minutes

Installing the library

Learn how to install our library in your system

7 minutes


See what documentation comes with your download

4 minutes

Main functionality

Here you will learn how to start using our library and unleash the power of Chebyshev in your computer. We strongly suggest you watch this video

16 minutes

Function Derivatives

See how to compute the derivatives of a function with our library

9 minutes


Learn how to serialize and deserialize MoCax Objects

4 minutes

Algebra of MoCaX Objects

You can sum MoCaX Objects, as well as multiply them by a number. This creates an algebra of Objects. Learn how to use it here

7 minutes


Our library allows you to build Splines within the Chebyshev approximation framework, easily. Learn how here

14 minutes

Slicing MoCaX Objects

See how you can slice MoCaX Objects of high dimensionality into simpler ones of lower dimensionality

5 minutes


Extrusion is the operation of MoCaX Objects by which you can expand its dimensionality. Learn how to do it here

5 minutes

Higher dimensions

Most of our examples are in only one dimension for illustrative purposes. Here you see how you can easily extend all features to higher dimensions

24 minutes


With our library, you can combine several MoCaX Objects into a single one via Slide Aggregation. In this way, problems of very high dimension can be tackled. Learn how to do it here

13 minutes

Maths and Methods

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

This is the first part of our 101 sessions on approximation theory and the maths behind the Chebyshev Spectral Decomposition techniques

20 minutes

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

This is the second part of our 101 sessions on approximation theory and the maths behind the Chebyshev Spectral Decomposition techniques

24 minutes

Evaluation of Chebyshev Objects

We describe here the way to evaluate Chebyshev Objects with minimum CPU load and no numerical instabilities

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

Coming Soon

Function Derivatives

With the Chebyshev methods, we can obtain all the partial derivatives of a function, up to very high orders. We explain how that is done

Algebra of Chebyshev Objects

We can add Chebyshev Objects* into a new object, as well as multiply it by a scalar. See how in this video

Discontinuities and Splines of Chebyshevs

In this video we discuss how to deal with discontinuities within the Chebyshev framework, as well as how to construct splines of Chebyshev interpolation frameworks

Maths of high-dimensional Chebyshev frameworks

The Chebyshev framework can be extended to any dimension. See how in this video

Accuracy prediction

Chebyshev methods offer us a way to know the accuracy of the approximation “ex-ante”; that is, before we evaluate the Chebyshev Object*. Here we explain how we can do that

Volatility surface calibration

Standard methods to calibrate volatility surfaces can be computationally expensive. Chebyshev provides a method to decrease such effort by orders of magnitude

Interpolating Grids

Interpolating grids are common practice in several calculations; for example market risk VaR. In this video, we show how the Chebyshev framework can build the same interpolating grids than other standard techniques (e.g. linear or spline interpolation) but with a fraction of the computing effort