  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.
