# Tail Risk Dynamics under Price-Limited Constraint: A Censored Autoregressive Conditional Fréchet Model

## TL;DR

This paper introduces a new model to study extreme financial risks in markets with price limits, showing how ignoring these limits can lead to underestimating risk.

## Contribution

A novel censored autoregressive conditional Fréchet model is proposed to analyze tail risk dynamics under price limits.

## Key findings

- Ignoring price limits leads to serious underestimation of tail risk in constrained markets.
- Widening price limits reduces extreme events but increases tail risk in the Chinese Taiwan stock market.
- Investors with different risk preferences may make opposing decisions during extreme events.

## Abstract

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management.