Historical Simulation, Variance-Covariance and Monte Carlo Simulation Methods for Market Risk Assessment: From NASDAQ Index 2015-2024

Market risk assessment is crucial for financial practitioners and helps manage potential losses from market volatility. This article compares three common VaR (value at risk) calculation methods - historical simulation, variance-covariance method and Monte Carlo simulation, and applies them to the past ten years of data of the Nasdaq Index. The results show that at a 95% confidence level, the VaR estimates given by these three methods are relatively close; however, at a 99% confidence level, the VaR values of Monte Carlo simulation and variance-covariance method are usually slightly higher than historical simulation. This shows that compared with historical simulation, these two methods are more sensitive to extreme market events and can more effectively capture tail risks when the market is volatile. In the future, machine learning technology is expected to improve the accuracy of VaR calculation, especially in dealing with high-dimensional data and complex nonlinear relationships.