Denting the FRTB IMA computational challenge via Orthogonal Chebyshev Sliding Technique

TL;DR

This paper presents a novel Orthogonal Chebyshev Sliding Technique using high-dimensional Chebyshev Tensors to significantly reduce computational costs in FRTB IMA capital calculations while maintaining high accuracy.

Contribution

The paper introduces a new Chebyshev-based approximation method that effectively reduces computational burden in financial risk capital calculations.

Findings

Over 90% reduction in computational time

High accuracy maintained in approximations

Validated within a tier-one bank system

Abstract

In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computational burden associated with the capital calculation as specified by FRTB IMA. In all cases, the computational burden reductions obtained were of more than $90\%$, while keeping high degrees of accuracy, the latter obtained as a result of the mathematical properties enjoyed by Chebyshev Tensors.