Analysis of Price Distribution of Financial Instruments: from Classic Models to Modern Adjustments

In this thesis, I explore advanced methodologies for enhancing the accuracy and reliability of financial modeling, particularly in the domains of stock price predictions, risk management, and option pricing. Traditional financial models often assume normally distributed returns, which fails to capture real-world financial data characteristics such as skewness and kurtosis. This discrepancy can lead to inaccuracies in risk management and derivative pricing. We incorporate Kernel Density Estimation (KDE) to derive a more accurate estimate of the underlying return distribution, leading to more precise risk measures and option prices. The methodology includes training KDE on historical log-returns, applying KDE-based models for Value at Risk (VaR) and Expected Shortfall (ES) estimation, simulating future stock prices, and calculating option prices using KDE-enhanced Monte Carlo simulations. Our results demonstrate that KDE-based models provide significant advantages over traditional models, offering more accurate and robust financial predictions.