This project explores four areas of quantitative finance: portfolio optimization, distribution analysis of returns, option price sensitivity, and pricing under stochastic volatility. First, portfolios of major tech stocks are optimized for low risk and high return, with the high-risk portfolio constrained to outperform Google’s historical returns. Next, tests on daily log-returns reveal deviations from normality indicating outliers. The third part analyzes the sensitivity of European option prices to input parameters. Finally, the Heston model is used to simulate non-constant volatility and evaluate delta-hedging strategies at varying frequencies. Results show that Black-Scholes pricing deviates significantly from simulated outcomes under stochastic volatility, while Heston-based values offer better alignment for quarterly and monthly hedging. The project combines empirical analysis and simulation to deepen understanding of financial modeling and risk.