To monitor risk in temporal financial networks, an understanding of how individual behaviours affect the temporal evolution of networks is needed. This is typically achieved using centrality and importance metrics, which rank nodes in terms of their position in the network. This approach works well for static networks, that do not change over time, but does not consider the dynamics of the network. In addition to this, current methods are often unable to capture the complex, often sparse and disconnected structures of financial transaction networks.
This thesis addresses these gaps by considering importance from a dynamical perspective, first by using spectral perturbations to derive measures of importance for nodes and edges, then adapting these methods to incorporate a structural awareness. I complement these methods with a generative model for transaction networks that captures how individual behaviours give rise to the key properties of these networks, offering new methods to add to the regulatory toolkit. My contributions are made across three studies which complement each other in their findings.
Study 1:
\begin{itemize}
\item I define a structural importance metric for the edges of a network, based on perturbing the adjacency matrix and observing the resultant change in its largest eigenvalues.
\item I combine this with a model of network evolution where this metric controls the scale and probabilities of subsequent edge changes. This allows me to consider how edge importance relates to subsequent edge behaviour.
\item I use this model alongside an exercise to predict subsequent change from edge importance. Using this I demonstrate how the model parameters are related to the capability of predicting whether an edge will change from its importance.
\end{itemize}
Study 2:
\begin{itemize}
\item I extend my measure of edge importance to measure the importance of nodes, and to capture complex community structures through the use of additional components of the eigenspectrum.
\item While computed from a static network, my measure of node importance outperforms other centrality measures as a predictor of nodes subsequently transacting. This implies that static representations of temporal networks can contain information about their dynamics.
\end{itemize}
Study 3:
\begin{itemize}
\item I contrast the snapshot based methods used in the first two studies by modelling the dynamic of transactions between counterparties using both univariate and multivariate Hawkes processes, which capture the non-linear `bursty’ behaviour of transaction sequences.
\item I find that the frequency of transactions between counterparties increases the likelihood of them to transact in the future, and that univariate and multivariate Hawkes processes show promise as generative models for transaction sequences.
\item Hawkes processes also perform well when used to model buys and sells through a central clearing counterparty when considered as a bivariate process, but not as well when these are modelled as individual univariate processes. This indicates that mutual excitation between buys and sells is present in these markets.
\end{itemize}
The observations presented in this thesis provide new insights into the behaviour of equities markets, which until now have mainly been studied via price information. The metrics I propose offer a new potential to identify important traders and transactions in complex trading networks. The models I propose provide a null model over which a user could detect outlying transactions and could also be used to generate synthetic data for sharing purposes
