Abstract
We propose a novel approach to calibrate the conditional value-at-risk (CoVaR) of financial institutions based on neural network quantile regression. Building on the estimation results, we model systemic risk spillover effects in a network context across banks by considering the marginal effects of the quantile regression procedure. An out-of-sample analysis shows great performance compared to a linear baseline specification, signifying the importance that nonlinearity plays for modelling systemic risk. We then propose three network-based measures from our fitted results. First, we use the Systemic Network Risk Index (SNRI) as a measure for total systemic risk. A comparison to the existing network-based risk measures reveals that our approach offers a new perspective on systemic risk due to the focus on the lower tail and to the allowance for nonlinear effects. We also introduce the Systemic Fragility Index (SFI) and the Systemic Hazard Index (SHI) as firm-specific measures, which allow us to identify systemically relevant firms during the financial crisis.
Highlights
The issue of systemic risk attracts a lot of attention from academics as well as from regulators in the aftermath of the financial crisis of 2007–2009
We propose the Systemic Network Risk Index (SNRI), a measure for the total systemic risk in the financial system which depends on the marginal effects, the outgoing VaRs, and the incoming conditional value-at-risk (CoVaR)
This paper proposes a novel approach to estimate the conditional value-at-risk (CoVaR) of financial institutions based on neural network quantile regression
Summary
The issue of systemic risk attracts a lot of attention from academics as well as from regulators in the aftermath of the financial crisis of 2007–2009. Adrian and Brunnermeier (2016) came up with conditional value-at-risk (CoVaR), a systemic extension of VaR Their original approach is restricted to analyse systemic risk in a linear and bivariate context. Our findings show that the quantile neural network-based approach provides a unique angle compared to the linear model for calibrating the systemic risk due to its flexibility. We estimate the VaR for each global systemically important financial institution (G-SIB) from the USA by regressing their stock returns on a set of risk factors using linear quantile regression. An out-of-sample comparison shows the superiority of our approach over a baseline model based on linear quantile regression This leads to the conclusion that nonlinear effects are crucial for the modelling of systemic risk.
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