Research on the Application of Extremum Theory in the Measurement of Extreme Volatility Risk in Financial Market

In the context of increasing complexity and volatility in global financial markets, in-depth analysis and precise measurement of extreme market fluctuations have become a critical task in risk management. Traditional methods, which assume that returns follow a normal distribution, fall short when describing actual market conditions where returns often exhibit fat-tail and leptokurtic characteristics. Extreme value theory, as a specialized statistical method for analyzing extreme events, offers a new perspective on the study of extreme market fluctuations. This paper comprehensively examines the application of extreme value theory in extreme market fluctuations from a risk measurement standpoint. It begins with an overview of the research background and significance, emphasizing the impact of extreme fluctuations on financial stability. The core principles of extreme value theory, including generalized extreme value distributions and generalized Pareto distributions, are then detailed. The empirical section collects long-term data from stock, foreign exchange, and other markets, preprocesses the data, and constructs tables to illustrate data characteristics, including return rates and extreme event data. The application of extreme value theory provides specific guidelines for analyzing extreme market fluctuations. Research findings indicate that extreme value theory can effectively capture extreme market fluctuations, offering more accurate tools for risk measurement. The conclusion summarizes the results, highlights the limitations of applying extreme value theory, and looks forward to future research directions, aiming to provide a reference for financial market risk management and regulation, addressing complex extreme fluctuation scenarios, and maintaining financial market stability.