This project is a combination of four mini projects. First, using six months of data from 100 large-cap stocks, log returns and volatilities were computed and then two optimized portfolios were constructed: Portfolio A (low-risk, profitable stocks) and Portfolio B (high-risk, high-return stocks), with volatility minimized using numerical methods. Second, log returns were tested for normality across time and after removing extremes using Shapiro-Wilk tests for various stocks/portfolios and even for the portfolio A and portfolio B from previous mini project. Third, graphs of call/put option prices vs time as well as spot price were studied. Fourth, Black-Scholes and Heston models were implemented to price options and simulate delta hedging under non-constant volatility. Profit distribution from the hedging strategy showed the effects of non-constant volatility and market dynamics.