We present an accurate and computationally efficient method, based on Chebyshev Spectral Decomposition, to stochastically compute the Initial Margin of financial products within a Monte Carlo simulation, via sensitivities simulation. This methodology is compared in terms of accuracy, efficiency, and implementation/maintenance costs with common techniques used for the same purpose, such as amortisation-based, regression-based and Adjoint Algorithmic Differentiation. Measured in terms of these criteria, the methodologies based on Chebyshev interpolants offer an optimal solution and set a new benchmark standard for the industry.
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