Counterparty Credit Limits: An Effective Tool for Mitigating Counterparty Risk?

A counterparty credit limit (CCL) is a limit imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. Although CCLs are designed to help institutions mitigate counterparty risk by selective diversification of their exposures, their implementation restricts the liquidity that institutions can access in an otherwise centralized pool. We address the question of how this mechanism impacts trade prices and volatility, both empirically and via a new model of trading with CCLs. We find empirically that CCLs cause little impact on trade. However, our model highlights that in extreme situations, CCLs could serve to destabilize prices and thereby influence systemic risk

Inference of Edge Correlations in Multilayer Networks

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent type of method for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but {potentially} inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By taking into account edge correlations, prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously-purchased grocery products

A framework for the construction of generative models for mesoscale structure in multilayer networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks

Community detection in temporal multilayer networks, with an application to correlation networks

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we study time-dependent financial-asset correlation networks. We first argue that the use of the "modularity" quality function---which is defined by comparing edge weights in an observed network to expected edge weights in a "null network"---is application-dependent. We differentiate between "null networks" and "null models" in our discussion of modularity maximization, and we highlight that the same null network can correspond to different null models. We then investigate a multilayer modularity-maximization problem to identify communities in temporal networks. Our multilayer analysis only depends on the form of the maximization problem and not on the specific quality function that one chooses. We introduce a diagnostic to measure \emph{persistence} of community structure in a multilayer network partition. We prove several results that describe how the multilayer maximization problem measures a trade-off between static community structure within layers and larger values of persistence across layers. We also discuss some computational issues that the popular "Louvain" heuristic faces with temporal multilayer networks and suggest ways to mitigate them.Comment: 42 pages, many figures, final accepted version before typesettin

Randomness and early termination: what makes a game exciting?

In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators? We study a terminal-boundary value problem for the nonlinear parabolic PDE $2\partial_te(t,x)=\log(-\partial_{xx}e(t,x))$ derived by Aldous and prove its wellposedness and regularity of its solution by combining PDE analysis and probabilistic tools, in particular the reformulation as a stochastic control problem with restricted control set, which allows us to deduce strict ellipticity. We establish key qualitative properties of the solution including concavity, monotonicity, convergence to a steady state for long remaining time and the asymptotic behaviour shortly before the terminal time. Moreover, we construct convergent numerical approximations. The analytical and numerical results allow us to highlight the behaviour of the win-probability process in the present case where the match may end early, in contrast to recent work by Backhoff-Veraguas and Beiglb\"ock where the match always runs the full length

Customer mobility and congestion in supermarkets

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales

The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market

We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with larger numbers of opportunities with shorter mean durations occurring during more liquid hours. We demonstrate further that the number of arbitrage opportunities has decreased in recent years, implying a corresponding increase in pricing efficiency. Using trading simulations, we show that a trader would need to beat other market participants to an unfeasibly large proportion of arbitrage prices to profit from triangular arbitrage over a prolonged period of time. Our results suggest that the foreign exchange market is internally self-consistent and provide a limited verification of market efficiency