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Chebyshev grid is a set of points on an interval. For example, on the interval [−1,1] the Chebyshev grid Cn consists of the points ...

Key words Chebyshev interpolation, parametric option pricing, high-dimensional problem, tensor train format, low-rank tensor approximation, tensor completion 1 Introduction Financial problems are, by their nature, multi- and high-dimensional, because a large number of risk factors contribute to the prices of each financial asset. Moreover, the

Finally we explain how Chebyshev Tensors can be used in the calculation of DIM and present DIM calculations obtained Chebyshev Tensors, Deep Neural Networks and other regression types. Pricing problem in risk calculations DIM, its challenges and different ways to compute it: Machine Learning, Chebyshev Tensors Chebyshev mathematical framework

Computationally easy to calibrate Highly accurate (e.g. 1e-5) Ultra-fast to evaluate The replica can be created via Chebyshev Tensors or Deep Neural Nets. Which is best depends on the details of the Monte Carlo engine and the portfolio. XVA calculations, as well as IMM capital and PFE simulations can be accelerated orders of magnitude on this way.

Nov 09, 2020 · This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. Dynamic sensitivities are then used to compute Dynamic Initial Margin as defined by ISDA (SIMM). The technique is benchmarked against the computation of dynamic sensitivities obtained by using pricing functions like the ones found in risk engines. We ...

Finally we explain how Chebyshev Tensors can be used in the calculation of DIM and present DIM calculations obtained Chebyshev Tensors, Deep Neural Networks ...

This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation.

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as and . They can be defined several equivalent ways; in this article the polynomials are defined by starting with trigonometric functions: The Chebyshev polynomials of the first kind are given by Similarly, define the Chebyshev polynomials of the second kind as

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.

Jul 03, 2017 · A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the surface in form of Chebyshev tensor product. This algorithm is based on the application of error-free transformations to improve the traditional Clenshaw Chebyshev tensor product algorithm.

08.12.2015 · Chebyshev Tensors and Machine Learning in DIM calc... ALCO Magazine - Issue #3, November 2018. ALCO Magazine - Issue #4, May 2020. The ALCO: making the most important bank committee... BTRM Working Paper Series, #11. BTRM Working Paper Series, #12. BTRM Working Paper Series, #13. BTRM Working Paper Series, #14. BTRM Working Paper Series, #15

Chebyshev tensors and how they are applied in risk engines. •. DIM calculations using Machine Learning techniques and Chebyshev tensors.

Dec 08, 2015 · Chebyshev Tensors and Machine Learning in DIM calc... ALCO Magazine - Issue #3, November 2018. ALCO Magazine - Issue #4, May 2020. The ALCO: making the most important bank committee... BTRM Working Paper Series, #11. BTRM Working Paper Series, #12. BTRM Working Paper Series, #13. BTRM Working Paper Series, #14. BTRM Working Paper Series, #15

09.11.2020 · Abstract:This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. Dynamic sensitivities are then used to compute Dynamic Initial Margin as defined by ISDA (SIMM). The technique is benchmarked against the computation of dynamic

This paper gives evidence that Chebyshev Tensors allow for timely and accurate calibration of expensive models such as the rough Bergomi (see [3]). This is done by approximating ’(Equation 2), restricted to the parameter set (space over which calibration is done), with a Chebyshev Tensor, and using this Chebyshev Tensor instead of ˚at calibration.

A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the ...

Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be approximated — due to their exponential convergence — the problem of calibration of pricing models seems, a priori, a good case where Chebyshev Tensors can excel.

Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be approximated — due to their exponential convergence — the problem of calibration of pricing models seems, a priori, a good case where Chebyshev Tensors can excel.

This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation.

Orthogonal Chebyshev Sliding Technique Mariano Zeron-Medina Laris∗ Ignacio Ruiz† December 10, 2020 A version of this paper has been peer-reviewed and will be published in Wilmott Magazine in January 2021. Abstract In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors called Orthogonal Chebyshev Sliding ...

Chebyshev Tensors and Machine Learning in DIM Calculations - Slides. In this presentation we see how Chebyhsev 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 Chebyhsev Tensors.

Chebyshev Tensors and Deep Neural Nets can be used to “clone” a pricing function from the pricing library to the risk engine. This can be optimally done when in conjunction with Composition Techniques or other dimensionality reduction methods.

03.07.2017 · A Chebyshev tensor product surface is widely used in image analysis and numerical approximation. This article illustrates an accurate evaluation for the surface in form of Chebyshev tensor product. This algorithm is based on the application of error-free transformations to improve the traditional Clenshaw Chebyshev tensor product algorithm.

Chebyshev polynomials are important in approximation theory because the roots of Tn(x), which are also called Chebyshev nodes, are used as matching points for ...

Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be ...