Four mini-projects explore key concepts in portfolio construction, stock distribution, option pricing, and hedging:

1. Using five years of ETF and stock data, we constructed high- and low-risk portfolios based on beta, pairwise correlation analysis, and mean-variance optimization from modern portfolio theory.

2. We tested whether log returns for JPMorgan Chase & Co. and our portfolio were normally distributed, applying Q-Q plots, box plots, and Shapiro-Wilk tests.

3. We analyzed European call and put options within the Black-Scholes framework, focusing on how prices and sensitivities evolve with time to expiration and underlying asset price movements.

4. We examined the effects of stochastic volatility (non-constant 𝜎) on hedging performance by simulating stock and volatility paths with the Heston model and evaluating different hedging strategies.