This project aggregates four quantitative finance mini-projects on portfolio construction, return distribution analysis, option Greeks, and hedging performance under realistic market conditions. First, I built high- and low-volatility portfolios, observing that higher volatility yields greater returns but with larger risks. Second, I tested the normality assumption of returns, finding portfolios approximate normal distributions, while individual stocks have heavier tails, implying underestimated tail risks. Third, I analyzed Black–Scholes Greeks, illustrating Delta, Gamma, and Vega sensitivities near at-the-money. Finally, I simulated delta hedging under stochastic volatility models (Regime-Switching, Heston, GARCH), revealing delta hedging alone cannot eliminate volatility-induced losses due to model misspecification and tail events. Overall, this project emphasizes understanding assumptions, distributional properties, and residual risks in portfolio and options management.