A coupled autoregressive extreme-value model for dynamic tail risk with risk spirals

This paper develops a coupled autoregressive conditional extreme-value model (AEV-H) for financial loss extremes. Relative to recent dynamic EVT specifications that allow tail-related parameters to vary over time, our model introduces an explicit cross-feedback structure between the conditional scale and tail index. The interaction terms allow conditional tail thickness to respond directly to volatility intensity, and vice versa, thereby providing a tractable way to study feedback effects between volatility intensity and tail risk in a conditional forecasting framework. We provide mild conditions under which the coupled system admits a unique stationary and geometrically ergodic solution. Empirically, using 5-minute CSI 300 index data, we find that the estimated interaction terms are economically and statistically meaningful, and that the filtered latent dynamics are consistent with a risk-spiral interpretation. Relative to the non-coupled benchmark, AEV-H also improves out-of-sample risk forecasting and backtesting performance. Additional cross-index evidence from the CSI 500 index and additional ES-based forecast evaluation provide further support for the main findings of the paper.