Melting Sensitivities - Exact and Approximate Margin Valuation Adjustments

44 Pages Posted: 5 Jan 2018 Last revised: 6 Mar 2018

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Peter Kohl-Landgraf

DZ Bank AG

Mario Viehmann

Ludwig Maximilian University of Munich (LMU)

Date Written: January 12, 2018

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.

Keywords: MVA, Initial Margin Simulation, ISDA SIMM, Automatic Differentiation, Adjoint Automatic Differentiation, Forward Sensitivities

JEL Classification: C15, G13, C63

Suggested Citation

Fries, Christian P. and Kohl-Landgraf, Peter and Viehmann, Mario, Melting Sensitivities - Exact and Approximate Margin Valuation Adjustments (January 12, 2018). Available at SSRN: https://ssrn.com/abstract=3095619 or http://dx.doi.org/10.2139/ssrn.3095619

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Peter Kohl-Landgraf

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Mario Viehmann

Ludwig Maximilian University of Munich (LMU) ( email )

Geschwister-Scholl-Platz 1
Munich, DE Bavaria 80539
Germany

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