Clearing Financial Networks with Derivatives: From Intractability to Algorithms

Financial networks raise a significant computational challenge in identifying insolvent firms and evaluating their exposure to systemic risk. This task, known as the clearing problem, is computationally tractable when dealing with simple debt contracts. However under the presence of certain derivatives called credit default swaps (CDSes) the clearing problem is $\textsf{FIXP}$-complete. Existing techniques only show $\textsf{PPAD}$-hardness for finding an $\epsilon$-solution for the clearing problem with CDSes within an unspecified small range for $\epsilon$. We present significant progress in both facets of the clearing problem: (i) intractability of approximate solutions; (ii) algorithms and heuristics for computable solutions. Leveraging $\textsf{Pure-Circuit}$ (FOCS'22), we provide the first explicit inapproximability bound for the clearing problem involving CDSes. Our primal contribution is a reduction from $\textsf{Pure-Circuit}$ which establishes that finding approximate solutions is $\textsf{PPAD}$-hard within a range of roughly 5%. To alleviate the complexity of the clearing problem, we identify two meaningful restrictions of the class of financial networks motivated by regulations: (i) the presence of a central clearing authority; and (ii) the restriction to covered CDSes. We provide the following results: (i.) The $\textsf{PPAD}$-hardness of approximation persists when central clearing authorities are introduced; (ii.) An optimisation-based method for solving the clearing problem with central clearing authorities; (iii.) A polynomial-time algorithm when the two restrictions hold simultaneously

Strategic Payments in Financial Networks

In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems

A formal analysis of complexity and systemic risk in financial networks with derivatives

The 2008 financial crisis has been attributed by policymakers to “excessive complexity” of the financial network, especially due to financial derivatives. In a financial network, financial institutions (“banks” for short) are connected by financial contracts. As banks depend on payments from contracts with other banks to cover their own obligations, such a situation creates systemic risk, i.e., the risk of a financial crisis. Some of the contracts are financial derivatives, where an obligation to pay depends on another variable. In this thesis, I study in what sense derivatives make a financial network fundamentally “more complex” compared to one without derivatives. I capture the notion of “complexity” formally using tools from finance and theoretical computer science. I reveal new kinds of systemic risk that arise in financial networks specifically because of derivatives and I discuss the impact of recent regulatory policy. I first focus on a type of derivative called a credit default swap (CDS), in which the writer insures the holder of the contract against the default (i.e., bankruptcy) of a third party, the reference entity. I show that, when the reference entity is another bank, then such CDSs introduce a new kind of systemic risk arising from what I call default ambiguity. Default ambiguity is a situation where it is impossible to decide which banks are in default following a shock (i.e., a loss in banks’ assets). At a technical level, I show that the clearing problem may have no solution or multiple incompatible solutions. In contrast, without CDSs, a unique canonical solution always exists. I then demonstrate that increased “complexity” due to CDSs also manifests as computational complexity. More in detail, I show that the clearing problem leads to NP-complete decision and PPAD-complete approximation problems if CDSs are allowed. This implies a fundamental barrier to the computational analysis of these networks, specifically to macroprudential stress testing. Without CDSs, the problems are either trivial or in P. I study the impact of different regulatory policies. My main result is that the aforementioned phenomena can be attributed to naked CDS positions. In a final step, I focus on one specific regulatory policy: mandatory portfolio compression, which is a post-trade mechanism by which cycles in the financial network are eliminated. While this always reduces individual exposures, I show that, surprisingly, it can worsen the impact of certain shocks. Banks’ incentives to compress may further be misaligned with social welfare. I provide sufficient conditions on the network structure under which these issues are eliminated. Overall, my results in this thesis contribute to a better understanding of systemic risk and the effects of regulatory policy

Too Interconnected To Fail: Financial Contagion and Systemic Risk in Network Model of CDS and Other Credit Enhancement Obligations of US Banks

Credit default swaps (CDS) which constitute up to 98% of credit derivatives have had a unique, endemic and pernicious role to play in the current financial crisis. However, there are few in depth empirical studies of the financial network interconnections among banks and between banks and nonbanks involved as CDS protection buyers and protection sellers. The ongoing problems related to technical insolvency of US commercial banks is not just confined to the so called legacy/toxic RMBS assets on balance sheets but also because of their credit risk exposures from SPVs (Special Purpose Vehicles) and the CDS markets. The dominance of a few big players in the chains of insurance and reinsurance for CDS credit risk mitigation for banks� assets has led to the idea of �too interconnected to fail� resulting, as in the case of AIG, of having to maintain the fiction of non-failure in order to avert a credit event that can bring down the CDS pyramid and the financial system. This paper also includes a brief discussion of the complex system Agent-based Computational Economics (ACE) approach to financial network modeling for systemic risk assessment. Quantitative analysis is confined to the empirical reconstruction of the US CDS network based on the FDIC Q4 2008 data in order to conduct a series of stress tests that investigate the consequences of the fact that top 5 US banks account for 92% of the US bank activity in the $34 tn global gross notional value of CDS for Q4 2008 (see, BIS and DTCC). The May-Wigner stability condition for networks is considered for the hub like dominance of a few financial entities in the US CDS structures to understand the lack of robustness. We provide a Systemic Risk Ratio and an implementation of concentration risk in CDS settlement for major US banks in terms of the loss of aggregate core capital. We also compare our stress test results with those provided by SCAP (Supervisory Capital Assessment Program). Finally, in the context of the Basel II credit risk transfer and synthetic securitization framework, there is little evidence that the CDS market predicated on a system of offsets to minimize final settlement can provide the credit risk mitigation sought by banks for reference assets in the case of a significant credit event. The large negative externalities that arise from a lack of robustness of the CDS financial network from the demise of a big CDS seller undermines the justification in Basel II that banks be permitted to reduce capital on assets that have CDS guarantees. We recommend that the Basel II provision for capital reduction on bank assets that have CDS cover should be discontinued.

Too Interconnected To Fail: Financial Contagion and Systemic Risk In Network Model of CDS and Other Credit Enhancement Obligations of US Banks

Credit default swaps (CDS) which constitute up to 98% of credit derivatives have had a unique, endemic and pernicious role to play in the current financial crisis. However, there are few in depth empirical studies of the financial network interconnections among banks and between banks and nonbanks involved as CDS protection buyers and protection sellers. The ongoing problems related to technical insolvency of US commercial banks is not just confined to the so called legacy/toxic RMBS assets on balance sheets but also because of their credit risk exposures from SPVs (Special Purpose Vehicles) and the CDS markets. The dominance of a few big players in the chains of insurance and reinsurance for CDS credit risk mitigation for banks’ assets has led to the idea of “too interconnected to fail” resulting, as in the case of AIG, of having to maintain the fiction of non-failure in order to avert a credit event that can bring down the CDS pyramid and the financial system. This paper also includes a brief discussion of the complex system Agent-based Computational Economics (ACE) approach to financial network modeling for systemic risk assessment. Quantitative analysis is confined to the empirical reconstruction of the US CDS network based on the FDIC Q4 2008 data in order to conduct a series of stress tests that investigate the consequences of the fact that top 5 US banks account for 92% of the US bank activity in the $34 tn global gross notional value of CDS for Q4 2008 (see, BIS and DTCC). The May-Wigner stability condition for networks is considered for the hub like dominance of a few financial entities in the US CDS structures to understand the lack of robustness. We provide a Systemic Risk Ratio and an implementation of concentration risk in CDS settlement for major US banks in terms of the loss of aggregate core capital. We also compare our stress test results with those provided by SCAP (Supervisory Capital Assessment Program). Finally, in the context of the Basel II credit risk transfer and synthetic securitization framework, there is little evidence that the CDS market predicated on a system of offsets to minimize final settlement can provide the credit risk mitigation sought by banks for reference assets in the case of a significant credit event. The large negative externalities that arise from a lack of robustness of the CDS financial network from the demise of a big CDS seller undermines the justification in Basel II that banks be permitted to reduce capital on assets that have CDS guarantees. We recommend that the Basel II provision for capital reduction on bank assets that have CDS cover should be discontinued.Credit Default Swaps; Financial Networks; Systemic Risk; Agent BasedCredit Default Swaps, Financial Networks, Systemic Risk, Agent Based Models, Complex Systems, Stress Testing

Default Ambiguity: Credit Default Swaps Create New Systemic Risks in Financial Networks

We study financial networks and reveal a new kind of systemic risk arising from what we call default ambiguity — that is, a situation where it is impossible to decide which banks are in default. Specifically, we study the clearing problem: given a network of banks interconnected by financial contracts, determine which banks are in default and what percentage of their liabilities they can pay. Prior work has shown that when banks can only enter into debt contracts with each other, this problem always has a unique maximal solution. We first prove that when banks can also enter into credit default swaps (CDSs), the clearing problem may have no solution or multiple conflicting solutions, thus leading to default ambiguity. We then derive sufficient conditions on the network structure to eliminate these issues. Finally, we discuss policy implications for the CDS market

Transaction Machines – The Infrastructure of Financial Markets

This thesis describes financial markets as complex machines in the broader sense, as systems for organizing informational flows and performing certain functions in regards to the processing of transactions. We focus on the transaction infrastructure of financial markets, on the flow architecture that allows transactions to happen in the first place. First, in order for a financial market to function there needs to be some mechanism for aggregating and matching disparate transactional requests. Another mechanism is then needed in order to untangle and reduce the complexity of overlapping exposures between participants. The history of finance shows us that there are indeed certain patterns and regularities, procedures and mechanisms present in any system that processes financial transactions. The thesis describes this sequence of functions as transaction machines, understood as complex socio-technical systems for the execution of financial transactions. This is achieved by leveraging a specific philosophical account of technology coupled with a computational and evolutionary account of financial markets. We ultimately focus two types of transaction machines, performing the matching and clearing of financial flows, acting as the infrastructure of financial markets. We also provide a sketch for an evolutionary trajectory of these machines, evolving under the demands and needs of marker participants. From medieval fairs to the millisecond electronic platforms of today, transaction machines have gradually transitioned from human-based ‘hardware’ to electronic automated platforms. Moreover, we also describe the complex power dynamics of contemporary transaction machines. In as much as they are the dominant hubs of global financial markets, the thesis argues for the necessity of a more granular account of the functioning and evolution of transaction machines