Research on the Application and Optimization of Mathematical Models in Financial Market Risk Management

University College London, UK

^* Corresponding author: luckpyy2025@163.com

Abstract

This paper applied mathematical models to conduct an in-depth discussion and empirical analysis of financial market risk management. The daily rate of return data on the S&P 500 index, selected through data processing, included data cleaning, return calculation, data standardization, construction of the GARCH (1, 1) model, and a Copula model for predicting and analyzing risks. Empirical results indicate that the GARCH model has good simulation in capturing the market volatility change, while the Copula model holds clear advantages in modeling multivariate risk dependencies. In the modern economy, managing risks in the financial market plays a vital role. Optimization algorithms such as genetic algorithms and Bayesian optimization significantly improve the prediction accuracy and computational efficiency of the model. Compared with traditional historical simulation methods, these models perform better in risk prediction indicators (VaR and ES), proving their practicality and effectiveness in actual risk management. The research results verify that advanced mathematical models and optimization methods have important application value in financial market risk management, providing a scientific decision-making basis for investors and risk managers.