  In this paper we offer a novel type of network model which can capture the
precise structure of a financial market based, for example, on empirical
findings. With the attached stochastic framework it is further possible to
study how an arbitrary network structure and its expected counterparty credit
risk are analytically related to each other. This allows us, for the first
time, to model the precise structure of an arbitrary financial market and to
derive the corresponding expected exposure in a closed-form expression. It
further enables us to draw implications for the study of systemic risk. We
apply the powerful theory of characteristic functions and Hilbert transforms.
The latter concept is used to express the characteristic function (c.f.) of the
random variable (r.v.) $\max(Y, 0)$ in terms of the c.f. of the r.v. $Y$. The
present paper applies this concept for the first time in mathematical finance.
We then characterise Eulerian digraphs as distinguished exposure structures and
show that considering the precise network structures is crucial for the study
of systemic risk. The introduced network model is then applied to study the
features of an over-the-counter and a centrally cleared market. We also give a
more general answer to the question of whether it is more advantageous for the
overall counterparty credit risk to clear via a central counterparty or
classically bilateral between the two involved counterparties. We then show
that the exact market structure is a crucial factor in answering the raised
question.
