Statistical Foundations and Machine Learning Perspectives in Quantitative Finance

Although advances in artificial intelligence (AI) and machine learning (ML) have transformed financial risk assessment, many early-warning frameworks for systematic risk still rely on isolated macro-financial indicators with limited integration of established statistical models. This study bridges that gap by incorporating classical quantitative financial methodologies such as the Capital Asset Pricing Model (CAPM), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Monte Carlo simulations within a modern data-driven analytical framework. Integrating these statistical methodologies into an early-warning system should improve its ability to detect both micro-level asset price dynamics and macro-level contagion trends, especially in emerging economies. This paper demonstrates how traditional models can complement AI- and ML-based predictive systems, enhancing the interpretability and robustness of early-warning mechanisms in finance. We apply these models to three notable stocks listed on Bursa Malaysia. Our analysis of market behaviour encompasses various theoretical dimensions, utilising daily data over a 10-year period from 2015 to 2024, resulting in 2,451 observations. CAPM evaluates systematic risk and anticipated returns via beta coefficients, GARCH models time-varying volatility and clustering phenomena, whilst Monte Carlo simulations generate probabilistic price paths under stochastic processes. The consolidated findings reveal varied risk-return characteristics among the equities, providing essential insights into volatility persistence, scenario-based forecasting, and portfolio optimisation. The analysis captures both micro-level asset dynamics and macro-level contagion effects. The results reveal distinct patterns in volatility persistence, systematic risk, and probabilistic return distributions. This paper demonstrates the empirical significance of each model and emphasises their theoretical foundations in contemporary finance literature. The results possess practical significance for investors, policymakers, and educators seeking to improve risk modelling, capital allocation, and financial decision-making in emerging economies.