Denting the FRTB‐IMA Computational Challenge via Orthogonal Chebyshev Sliding Technique

Abstract

In this paper we introduce a new technique based on high-dimensional Chebyshev tensors, called the orthogonal Chebyshev sliding technique. We implemented this technique inside the systems of a tier-one bank to approximate front-office pricing functions with the aim of reducing the substantial computational burden associated with the FRTB-IMA capital calculation. In all cases, the computational burden reductions obtained were of more than 90 percent, while keeping high degrees of accuracy. The latter obtained as a result of the mathematical properties enjoyed by Chebyshev tensors.

Dynamic sensitivities and Initial Margin via Chebyshev Tensors

“…Once built, they are evaluated very efficiently. Chebyshev Tensors have already been shown to accelerate a wide range of risk calculations (see [9], [10], [3], [4]). In this paper, we use them to compute sensitivities within a Monte Carlo engine (dynamic sensitivities).…”