# Videos & Tutorials

See it with your own eyesIn 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

# Introductions…

# The library

# Mathematics of Chebyshev Methods

#### Evaluation of Chebyshev Objects

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

#### 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

#### 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

#### Higher Dimensions

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

# Applications

#### Dynamic Sensitivities and Initial Margin

Chebyshev provides the tools for an accurate and ultra-fast stochastic simulation of dynamic sensitivities and Initial Margin

#### 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

#### FRTB

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

#### 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

#### 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