This project presents a collection of four studies applying core principles of quantitative finance to practical market problems. The work encompasses: (1) Markowitz mean-variance optimization to construct portfolios with targeted risk-return profiles; (2) statistical hypothesis testing to investigate the common assumption of normality in log returns; (3) sensitivity analysis of the Black-Scholes model to visualize option Greeks; and (4) simulation of delta hedging strategies under various stochastic volatility models.