Systemic Greeks: Measuring risk in financial networks

TL;DR

This paper introduces a network-based approach to measure systemic risk in financial networks by extending traditional credit risk models and defining a new systemic risk sensitivity measure called network Δ.

Contribution

It develops a formal framework for computing Greeks in financial networks and proposes the network Δ as a novel quantitative systemic risk indicator.

Findings

Network Δ effectively measures systemic risk sensitivity.

Extended credit risk models incorporate network effects.

Numerical examples demonstrate the utility of the proposed measure.

Abstract

Since the latest financial crisis, the idea of systemic risk has received considerable interest. In particular, contagion effects arising from cross-holdings between interconnected financial firms have been studied extensively. Drawing inspiration from the field of complex networks, these attempts are largely unaware of models and theories for credit risk of individual firms. Here, we note that recent network valuation models extend the seminal structural risk model of Merton (1974). Furthermore, we formally compute sensitivities to various risk factors -- commonly known as Greeks -- in a network context. In particular, we propose the network $\Delta$ as a quantitative measure of systemic risk and illustrate our findings on some numerical examples.