Volatility estimation and crash risk forecasting using unified GARCH models: Empirical evidence from the Russian invasion of Ukraine

Given the significant impact on economies and financial markets, this study aims to effectively estimate stock return volatilities related to the Russian invasion of Ukraine on February 24, 2022. To achieve this, we developed fully unified generalized autoregressive conditional heteroscedasticity (GARCH) models based on behavioral finance theories that incorporate asymmetry, skewed distribution errors, and structural breaks. Using daily samples from July 2020 to March 2025, which include the impact of the Russian invasion, we first revealed that our fully unified GARCH models are effective in estimating Russian stock market index return volatilities, demonstrating the efficacy of our model unification approach. Additionally, using two other sets of daily 1,000 samples up until one week before or four weeks before the Russian invasion, we found that both one week and four weeks before the invasion, our fully unified GARCH models more effectively predicted the soaring Russian stock market volatilities affected by the Russian invasion. This shows the ability of our fully unified GARCH models to predict crash risk in the Russian stock market, which is one of the most novel pieces of evidence from our work. Furthermore, for the Russian stock index, the volatility estimates from our fully unified GARCH models have shown predictive power for the volatilities of non-fully unified models, while those from non-fully unified models do not predict the volatilities of the fully unified models. This finding also demonstrates the novelty of our work. Moreover, we provided numerous valuable interpretations, implications, and innovative perspectives for future research and practice of quantitative finance and economics. Furthermore, we emphasize that, in addition to extending GARCH models, this paper offers: (i) insight into the link between models, theory, and real-world data; (ii) perspectives on the relationship between information, human psychology, and structural breaks; and (iii) valuable broader implications of the impacts of Russia's invasion of Ukraine. These novel insights are crucial and will inspire future research across multiple disciplines.