Computing the Probability of a Financial Market Failure: A New Measure of Systemic Risk
Jarrow, R., Protter, P. & Quintos, A. Computing the probability of a financial market failure: a new measure of systemic risk. Ann Oper Res (2022). https://doi.org/10.1007/s10479-022-05146-9
31 Pages Posted: 25 Oct 2021 Last revised: 24 Dec 2022
Date Written: October 21, 2021
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.
Keywords: Systemic risk, market failure probabilities, G-SIBs, multivariate Cox processes
JEL Classification: C02, C60, G32
Suggested Citation: Suggested Citation