Melting Sensitivities - Exact and Approximate Margin Valuation Adjustments

Abstract

In this paper we present various methods for fast and accurate calculation of margin valuation adjustments (MVA). We consider the calculation of an MVA using sensitivities for the determination of the initial margin and consider the IDSA SIMM (ISDA Standard Initial Margin Model) as a benchmark. To assess the quality of the various approximations we calculate an - up to Monte-Carlo and discretization errors - exact MVA applying adjoint algorithmic differentiation (AAD). This exact MVA and exact forward initial margin serves as a benchmark for the various approximation methods. It turns out that the conversion from model sensitivities to market rate sensitivities - as required by SIMM - constitutes a computationally expensive calculation step. The step requires the calculation of a (pseudo-) inverse of stochastic matrices. We therefore introduce approximation methods allowing for more efficient MVA calculation.