**Chebyshev Spectral Decomposition for Ultra-efficient Risk Calculations by Ignacio Ruiz**

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**Presenter: Ignacio Ruiz, Founder & CEO of MoCaX Intelligence**

- The power of Chebyshev – MoCaX as a Smart interpolation scheme
- Selection of interpolating points and functions
- Chebyshev nodes and Chebyshev polynomials in the context of Risk Calculations
- Theoretical basis: three fundamental theorems
- Example: Parametric Chebyshev interpolation for Risk Calculations
- Practical cases studies:
- CVA
- CVA on exotics
- Cost effective IMA-FRTB (passing P&L Attribution tests!)
- Dynamic Initial Margin
- Accurate MVA
- Ultra-fast XVA sensitivities

- Commercial benefits: reduction of hardware costs, effective computation of risk metrics, hedging regulatory risk
- Generic AAD via Chebyshev Decomposition