Applications of Matrix Methods in Financial Risk Analysis

Financial risk analysts use historical time series data that details financial market factors to analyze stock prices, to measure general risk factors, and to build financial portfolios. We use daily stock closing prices as our data for creating correlations. The correlation matrix must be positive definite. When a correlation matrix is not positive-definite, we perform a spectral decomposition of the original correlation matrix and then undertake a nearest matrix search to find a nearest correlation matrix which is positive-definite. With this new positive definite matrix we can run a Monte Carlo simulation to estimate Value at Risk for the portfolio. Python is used for data collection, numerical calculations, and testing the positive-definiteness of the output matrices.