New model tracks extreme financial risk with single parameter
A new framework models and tracks extreme financial risk over time using a single integrated tail shape parameter. It simplifies the assessment of Value-at-Risk (VaR) and Expected Shortfall (ES) for financial institutions and regulators.
Simplifying extreme tail dynamics
The paper introduces a robust semi-parametric framework for time-varying extreme tail behavior, including Value-at-Risk (VaR) and Expected Shortfall (ES).
Unlike previous models, this framework uses a conditional Generalized Pareto Distribution (GPD) for peaks-over-threshold (POT) dynamics, rescaled by their thresholds.
This allows the entire tail to be described by a single time-varying shape parameter, significantly reducing model complexity.
The time variation in this parameter follows integrated score-driven dynamics, enabling the capture of highly persistent, near-unit-root behavior in tail risk, which existing approaches often fail to address.
The model remains statistically well-behaved, stationary, and ergodic under mild conditions, with parameters consistently estimable using maximum likelihood techniques.
Real-world application and policy tools
The model's practical application is demonstrated using hourly Bitcoin and Ether returns from 2018 to 2025. This empirical analysis shows the tail-shape parameter varying significantly, effectively detecting pronounced increases in tail risk during 2022, coinciding with major cryptocurrency collapses such as Terra/Luna and FTX.
Out-of-sample comparisons indicate that the single-parameter model performs competitively against more complex dynamic Extreme Value Theory (EVT) specifications and often surpasses standard GARCH models, particularly in the extreme tail.
This framework offers policy economists and risk managers a practical and statistically consistent tool for monitoring extreme market risk, providing data-driven estimates for capital adequacy and systemic risk monitoring.