Abstract:

The increasing global economic uncertainty and the frequent occurrence of extreme events have made the precise measurement of extreme risk spillover effects in global stock markets a crucial approach for addressing cross-border financial shocks. Existing studies exhibit certain limitations in comprehensively considering the nonlinearities， long-term dependencies， and multivariable interactive effects of time series. Therefore， a Transformer-LSTM quantile regression model is proposed that leverages the multi-head attention mechanism in the Transformer to process multiple attention mechanisms in parallel， while extracting the temporal characteristics of the data. This approach aims to more accurately capture the temporal evolution of extreme risks in global stock markets and examine risk spillover effects during the full sample period and crisis periods such as a financial crisis through constructing spillover networks. Based on empirical results from weekly stock index data of 19 countries from December 2001 to March 2024， the findings are as follows： （i） The proposed model demonstrates superior predictive power compared to the Multilayer Perceptron （MLP）， Long Short-Term Memory （LSTM） network， and Transformer models. （ii） The spillover effects in cross-country stock markets exhibit asymmetry over the full sample period. Notably， there is a significant risk spillover effect in the U.S. stock market， while Chinese stock market shows no obvious risk spillover or receiving effects. （iii） During crisis events， extreme risk spillovers increase and asymmetry intensifies. During the financial crisis， the risk spillover effects from the U.S. are significant， with notable bidirectional spillover across multiple countries’ stock markets. During the European debt crisis， risk spillover effects are primarily concentrated in European countries’ stock markets. The risk impact from the U.S. stock market on China notably strengthens during the Sino-US trade friction. During the COVID-19 pandemic， stock markets of developed countries such as the U.S. and the U.K. remain the main sources of risk spillover. The proposed model offers new insights into capturing the extreme risk spillover in financial markets， which is important for risk management in global stock markets during times of crisis.

Key words: global stock markets, extreme risk spillover, CoVaR, Transformer-LSTM, quantile regression, spillover network