Computing the Probability of a Financial Market Failure: A New Measure of Systemic Risk

TL;DR

This paper introduces a new probabilistic measure for systemic risk by modeling the joint default probability of key banks using a multivariate Cox process, highlighting conditions leading to inevitable market failure.

Contribution

It develops a novel intensity-based framework to quantify the probability of market failure involving multiple G-SIBs, including theoretical results and implications for systemic risk assessment.

Findings

Market failure probability increases with the number of G-SIBs.

The probability tends to 1 when the number of G-SIBs is large.

Derived theorems relate market failure to initial economic conditions.

Abstract

This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. The characterization employs a multivariate Cox process across the G-SIBs, which allows us to relate our work to the existing literature on intensity-based models. Various theorems related to market failure probabilities are derived, including the probability of a market failure due to two banks defaulting over the next infinitesimal interval, the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to 1.