A systemic change of measure from central clearing

• Published date: 01 September 2022
• Author: Injun Hwang,Baeho Kim
• Date: 01 September 2022
• DOI: http://doi.org/10.1002/fut.22300

Received: 28 November 2021

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Accepted: 4 December 2021

DOI: 10.1002/fut.22300

RESEARCH ARTICLE

A systemic change of measure from central clearing

Injun Hwang |Baeho Kim

Korea University Business School, Seoul,

Republic of Korea

Correspondence

Baeho Kim, Korea University Business

School, Anam‐dong, Seongbuk‐Gu, Seoul

02841, Republic of Korea.

Email: baehokim@korea.ac.kr

Abstract

This study investigates the systemic impact of central clearing based on a

financial network model in which edge weights represent the sensitivities of

one participant's failure to its counterparties' default likelihood. The reduced‐

form model specifies the mechanism of systemic risk concentration under

central clearing in that a central counterparty redistributes the probability

mass of the systemic failure from the center of the distribution into its tail.

Numerical illustrations shed light on implications for regulating the adverse

dependence between risk concentration under central clearing and the re-

siliency of the financial system via proper margin schemes.

KEYWORDS

central clearing, margin policy, measure change, Monte Carlo simulation, systemic risk, tail

risk concentration

1|INTRODUCTION

Central counterparty clearing (CCC) can be traced back to the beginning of the modern banking system in the 18th

century when it was used to exchange checks and coins. However, this method of the clearing was prone to error and

abuse. Around 1770, bank clerks in London began to meet at Five Bells, a tavern on Lombard Street, to exchange all

their checks and settle their balances in cash (Nevin & Davis, 1970). In the 19th century, CCC arrangements became

popular in production and stock exchanges in the United States and Europe (Emery, 1896). In today's financial

markets, CCC arrangements are used to settle transactions for various derivatives, securities, and money markets. They

operate by inserting a central counterparty (CCP) between every pair of market participants.

Systemic risk often refers to the likelihood of observing a cascade of failures in a financial system. Central clearing

has been introduced to mitigate such risks by isolating financial institutions from their counterparty credit risk.

Consequently, recent financial regulations have pushed for the introduction of CCPs into various markets to reduce

complexity and enhance transparency and stability. Nevertheless, by becoming a nexus of netting and the sole absorber

of default impacts, a default by the CCP may cause uncontrollable credit risk propagation through a centralized

network. In this regard, the default of a Nasdaq Clearing Commodities member in 2018 and the ongoing COVID‐19

market turbulence underscore the importance of holistic risk management practices by the CCP to forestall the loss

spread at the systemic level.

This study investigates the trade‐off between the system‐wide cost and the benefit of central clearing when con-

sidering counterparty default risk. While CCPs are intended to reduce systemic risk in the financial system, the

centralized approach inherent in CCC arrangements can also lead to a concentration of risk for financial markets. In

other words, CCPs are systemically important interconnectors in the financial system as their operations transform

systemic risk. Notably, introducing a CCP into a market redistributes the probability mass of system‐wide defaults from

the center of the distribution to its tail. Thus, the centrality of a CCP leads to a concentration of risk accompanied by

contagion effects based on mutually strengthening interactions with the source of systematic risk. We use a probability

J Futures Markets. 2022;42:1738–1754.wileyonlinelibrary.com/journal/fut1738

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© 2022 Wiley Periodicals LLC

measure change technique to drive the distributional changes in the aggregate default rate induced by introducing the

CCP and initial margin schemes. Trade‐offs often appear between a CCP's benefit from margin collection, isolating

clearing members (CMs) from other CMs' defaults, and the cost of joining central clearing. For example, reducing the

first moment of the total number of defaults under a central clearing arrangement often has an adverse effect on its tail

risk. We provide meaningful implications by showing how the margin policy design can mitigate CCP‐driven systemic

risk concentration.

Duffie and Zhu (2011) pioneered research on central clearing and its netting efficiency. They show that expected

aggregate exposure may arise from central clearing as a trade‐off result in a model in which multilateral netting

through the CCP deprives netting opportunities across noncentrally cleared contracts. Cont and Kokholm (2014) relax

the assumptions in Duffie and Zhu (2011) and derive more plausible conditions for efficient multilateral netting.

Menkveld (2017) employs the framework of Duffie and Zhu (2011) and turns the focus onto the total exposure of the

CCP against CMs to investigate how the concentration of positions can cause distress to the CCP. Additionally, Garratt

and Zimmerman (2020) examine the mean‐variance of the expected exposure under financial network structures,

revealing that there is a strict subset relation among networks.

This strand of literature recognizes the vital role of CCPs in mitigating and managing systemic risk; however, the

likelihood of systemic default clustering under central clearing has not been properly investigated. Our study attempts to fill

this gap by specifying a stochastic default intensity model. Our proposed model framework sheds light on the impact of

introducing central clearing into a financial market of participants in the presence of counterparty default risk. Specifically,

we posit a network in which edge weights represent the sensitivities of one counterparty's failure to another participant's

default likelihood under bilateral arrangements. The (potentially dynamic) interdependency drives contagion in this net-

work, with defaults jointly correlated via an intensity‐based model. It is worth mentioning that the general description of the

bilateral model provides sufficient details to ensure that a meaningful central clearing entity (i.e., CCC) can be introduced in

the system. Accordingly, we apply a well‐defined intensity‐based default model under central clearing. The procedure

entails a change of measure under which one can appropriately address the systemic contribution of CCP in the system as a

whole, and the probability measure change is driven by the likelihood ratio of the modified measure under CCC divided by

the original probability measure under the bilateral arrangement. The bilateral and CCC models are consistent such that

direct comparisons can be analyzed in the context of risk concentration.

The central quantity of our investigation is the distribution of the aggregate default rate, defined as the number of

defaults divided by the total number of participants in the system. The statistical properties of the total number of

defaults for a fixed time horizon can be deduced via Monte Carlo (MC) simulation in the setting of bilateral and

centrally cleared markets with the application of a novel importance sampling technique for tail probability estimation.

Our findings indicate that introducing a CCP to a bilateral counterparty arrangement has nontrivial effects on the tail

distribution of the aggregate default rate. Moreover, this tail distribution shows nontrivial dependence on the margin

policy, along with the protocol for CCP default proceedings. Our intensity‐based network model allows a framework

under which trade‐offs arise before and after the introduction of central clearing. In this context, we further investigate

the optimal risk management of the CCP in totalizing and minimizing systemic risk to provide meaningful implications

by showing how we can mitigate the CCP‐driven systemic risk concentration.

Our main findings show that systemic trade‐offs may appear under the central clearing scheme, as reducing the first

moment of the aggregate default rate often has an adverse effect on the tail risk and vice versa. Central clearing is more

likely to decrease the mean of the aggregate default rate if the CCP protects survivors against counterparties' defaults.

However, delayed default feedback may cause the clustering of failures once the CCP defaults. A systemic risk

concentration arises due to the lowering of the average default rate in regular time. Given a reasonable choice of

preference parameter sets governing the policymaker's priorities over different goals to achieve, inactive, and proactive

margin schemes generally dominate a reactive margin scheme. Moreover, as the survivor probability of the CCP is

backed better by the inactive and proactive margin schemes, there remain fewer reasons to adhere to reactive margin

schemes.

2|STATISTICAL MODEL FORMULATION

In this section, we posit a reduced‐form network in which the edge weights represent the sensitivities of one coun-

terparty's failure to another participant's default likelihood. The potentially dynamic interdependence structure drives

the contagion in the network with defaults jointly correlated via an intensity‐based model.

HWANG AND KIM

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