Dynamic Initial Margin Estimation Based on Quantiles of Johnson Distributions

24 Pages Posted: 23 Mar 2018 Last revised: 15 Nov 2022

See all articles by Thomas McWalter

Thomas McWalter

University of Cape Town (UCT); University of Johannesburg

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); acadia

Nikolai Nowaczyk

AcadiaSoft

Ralph Rudd

The African Institute of Financial Markets and Risk Management

Sarp Kaya Acar

Quaternion Risk Management

Multiple version iconThere are 2 versions of this paper

Date Written: September 24, 2018

Abstract

The estimation of dynamic initial margin (DIM) is a challenging problem. We describe an accurate new approach using Johnson-type distributions, which are fitted to conditional moments, estimated using a least-squares Monte Carlo simulation (the JLSMC algorithm). We compare JLSMC DIM estimates with those computed using an accurate nested Monte Carlo simulation as a benchmark, and with another method that assumes portfolio changes are Gaussian. The comparisons reveal that the JLSMC algorithm is accurate and efficient, producing results that are comparable with nested Monte Carlo while using an order of magnitude less computational effort. We provide illustrative examples using the Hull-White and Heston models for different derivatives and portfolios. A further advantage of our new approach is that it relies only on the readily available data that is needed for any exposure or XVA calculation.

Keywords: dynamic initial margin (DIM); margin value adjustment (MVA); quantiles; Johnson distributions; least squares Monte Carlo.

JEL Classification: G12, G13

Suggested Citation

McWalter, Thomas and Kienitz, Joerg and Nowaczyk, Nikolai and Rudd, Ralph and Acar, Sarp Kaya, Dynamic Initial Margin Estimation Based on Quantiles of Johnson Distributions (September 24, 2018). Available at SSRN: https://ssrn.com/abstract=3147811 or http://dx.doi.org/10.2139/ssrn.3147811

Thomas McWalter (Contact Author)

University of Cape Town (UCT) ( email )

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University of Johannesburg ( email )

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Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

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University of Cape Town (UCT) ( email )

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Nikolai Nowaczyk

AcadiaSoft ( email )

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Ralph Rudd

The African Institute of Financial Markets and Risk Management ( email )

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Sarp Kaya Acar

Quaternion Risk Management ( email )

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Ireland

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