Dynamic Initial Margin Estimation Based on Quantiles of Johnson Distributions

21 Pages Posted: 23 Mar 2018 Last revised: 20 Jan 2021

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); Quaternion Risk Management

Nikolai Nowaczyk

Quaternion Risk Management

Ralph Rudd

The African Institute of Financial Markets and Risk Management

Sarp Kaya Acar

Quaternion Risk Management

Date Written: September 24, 2018

Abstract

The estimation of dynamic initial margin (DIM) for general portfolios is a challenging problem. The present paper describes an accurate new approach, based on regression, that uses Johnson-type distributions, which are fitted to conditional moments estimated using least-squares Monte Carlo simulation (the JLSMC approach). This approach is compared to DIM estimates computed using nested Monte Carlo as a benchmark. Under a number of test cases, the two approaches are shown to be coherent. Furthermore, we show that estimates of DIM produced under the standard regression approach, which assumes portfolio changes are Gaussian, diverges significantly from the better estimates using the JLSMC and nested Monte Carlo approaches. The standard approach performs particularly poorly if the portfolio changes are far from Gaussian (e.g. for options). To further demonstrate the efficacy of the JLSMC approach we provide illustrative examples using Hull-White and Heston models for different derivatives and portfolios. A further advantage of the new approach is that it only relies on the quantities required for any exposure or XVA calculation.

Keywords: Dynamic Initial Margin, Least Squares Monte Carlo, Johnson Distributions

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 )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

University of Johannesburg ( email )

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Johannesburg, Gauteng 2006
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Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

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42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

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Dublin, D02X308
Ireland

Nikolai Nowaczyk

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Ralph Rudd

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

Leslie Commerce Building
Rondebosch
Cape Town, Western Cape 7700
South Africa
+27 21 650 2474 (Phone)

Sarp Kaya Acar

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

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