Clearing Systems and the Transmission of Systemic Risk

Larry Eisenberg
The Risk Engineering Company, East Brunswick, NJ
eyes@panix.com

Thomas H. Noe
Department of Finance, Georgia State University
tomnoe@gsu.edu

Abstract

One of the most pervasive aspects of the contemporary financial environment is the rich network of interconnections between firms. Although financial liabilities owed by one firm to another are usually modeled as unidirectional obligations dependent only on the financial health of the issuing firm, in reality the liability structure of corporate obligations is invariably much more intricate. The value of what one firm owes another is, however, not independent of the values of debt issued by other firms in the financial network. The value of most firms is dependent on the payoff from financial claims on other firms. The value of these claims depends in turn on the financial health of yet other firms in the system. Moreover the linkages between firms are reciprocal, a default by firm A on its obligations to firm B may lead B to default on its obligations to C. C's default may, in turn, have a feedback effect on A. These interconnections are particularly salient when firms are part of a single clearing mechanism in which the repayment obligations of all firms within the system are determined simultaneously in fashion consistent with the priority of debt claims and the limited liability of equity.

All markets have some kind of clearing mechanism. Perhaps clearing mechanisms for interbank payments and for listed exchanges have received the most attention. In the United States, CHIPS and Fedwire are the main banking clearing mechanisms. In Germany, for example, there the Abrechnung and the EAF (Elektronische Abrechnung mit Filetransfer). Regards clearing mechanisms, one of the attractions of trading on a listed options exchange, the CBOE for example, is that the Options Clearing Corporation is the counterparty to every trade. Hence credit considerations do not prohibit lower credit traders from participating in these markets. There are many examples where the failure or potential failure of a firm coupled with the knowledge that the financial health of firms is interconnected has been cause for public attention. Examples in payments systems include: the failure of I.D. Herstatt in 1974 and the Bank of New York overnight shortfall of 22.6 billion dollars in 1985. Regarding listed exchanges, there is the crash of 1987. Other examples include: the bankruptcy of Olympia and York, the failure of the Bank of New England, the collapse of the Tokyo real estate market, the bankruptcy and public bailout of American S&L's to the cost of about 500 billion dollars and the Venezualian bank crisis of 1994.

Surprisingly, despite the obvious importance of the "architecture of financial linkages" for the determination of the return-generating process for financial assets, little has been written on this topic prior to a paper written by one of the authors [Eisenberg, "Boolean Networks and Financial Network Shutdown," Santa Fe Institute, 1994]. This is even more surprising given the extensive literature modeling default in a simple unidirectional context. In fact the whole literature on term-structure starting with Merton's 1973 article on option pricing ignores the considerations mentioned above. While modeling the valuation of a firm's debt as independent from that of other firms simplifies debt and equity models, this assumption becomes questionable in portfolio management, corporate bond trading and the analysis of counterparty credit risk. The aim of this paper is to investigate the propagation of risk through clearing systems and the effects of this risk propagation on the return-generating process of system-participants.

To address this problem, we will develop a fairly general model of a clearing system. We will show, via a fixed-point argument, that there always exists a "clearing payment vector," specifying the total payment made by each node in the system, which clears the obligations of the members of the clearing system. That is, all payments are consistent with each other, the simultaneous nonlinear constraints of the clearing mechanism.

Next, we perform comparative statics on this clearing payment vector, determining the nature of its dependence of the vector of exogenous cash infusions received by firms within the system as well as its dependence on the architecture of financial liabilities linking the various members of the system. More specifically, we show that the clearing payment vector is a multidimensional concave function of operating cash flows and the level of nominal payments. Further, the clearing system exhibits quasiconcavity. In other words, a clearing system which is a convex combination of two clearing systems, always produces payment vectors less the upper bound and greater than the lower bound of the two systems payment vectors. Stronger concavity results are shown not to hold in general via counterexamples.

To further analyze financial architecture, we consider in detail further properties of the clearing system architecture, focusing on the "relative exposure matrix", whose entries represent the dependence of a node on receiving payment from one of its debtors in meeting its own obligations. Using this matrix we address a number of issues of financial network performance. We develop the concept of "structural solvency." Structural solvency represents the cents on the dollar each node in the system is able to pay on its obligations even in the absence of any exogenous cash infusions. Structural solvency places a lower bond on the magnitude of defaults in the financial system. We then consider the relationship between structural solvency and the "fundamental solvency", measured by the ratio of the debt to equity of each of the nodes in the system.

The results obtained from this analysis are then used to derive conditions under which bilateral netting between members of the clearing network increases the average solvency of the financial system. Next, we characterize how an increase in volatility of underlying earning is translated into volatilities of clearing payment vectors. We also present several measures of systemic risk which indicate how the network, viewed as a filter which processes exogenous equity to the network increases or reduces sytemic risk in the debt and equity markets of the firms in the network.

Finally, these characterizations of the return generating process, are used both to characterize the effect of shocks to the financial system on stock betas and to deriving a pricing model for risky debt written on firms belonging to the same clearing network.