Research on the Impact and Applications of Financial Mathematics in Modern Financial Markets

With increasing volatility in global financial markets and the rapid development of complex trading strategies, the importance of financial mathematics in asset pricing, risk measurement, and investment decision-making has become increasingly evident. Stochastic process models offer systematic methods for characterizing dynamic asset price movements, capturing both short-term fluctuations and long-term trends, while risk assessment and pricing models provide a quantitative foundation for evaluating market uncertainty and guiding investment strategies. This study explores the role of financial mathematics in modern markets by examining the fundamental mechanisms behind price fluctuations and the stability of market risk, supported by empirical analysis that considers the proportion of quantitative model application alongside established market volatility indices. The results demonstrate that an appropriately moderate application of financial mathematical tools can effectively mitigate overall market volatility and promote more efficient allocation of resources across different financial instruments and sectors. Conversely, when the use of quantitative models is highly consistent or overly concentrated, short-term volatility may temporarily increase, exerting transient pressure on market stability. These findings highlight the nuanced impact of financial mathematics, indicating that while these tools are essential for informed decision-making and risk management, their implementation requires careful calibration to avoid unintended destabilizing effects on financial markets.