This project consists of four mini-projects covering portfolio construction, normality testing, option pricing, and delta hedging with time-varying volatility. I used real stock data to build high- and low-risk portfolios, statistically tested the normality of log returns, and implemented Black-Scholes delta hedging. In the final project, I explored the impact of GARCH-generated volatility on hedging performance compared to constant volatility, gaining deeper intuition on real market behavior. Out of personal curiosity, I also considered how a hybrid approach might integrate discrete GARCH volatility into simulation frameworks like Heston. This project helped solidify my understanding of core quantitative finance concepts through hands-on modeling and analysis.