Mini-Project 1: Portfolio Optimization:
- Implement Markowitz Portfolio Theory: Compute maximum Sharpe ratio and minimum volatility portfolios.
- Explore LLM-based portfolio selection.
- Build a simple backtesting system for trading agents.

Mini-Project 2: Non-Normal Returns
- Investigate the failure of the Black-Scholes assumption that log returns follow a normal distribution in real markets.
- Discuss the causes and implications of fat-tailed distributions in financial returns.

Mini-Project 3: Option Pricing
- Revisit the Black-Scholes PDE as an inverse heat equation.
- Calculate and interpret option Greeks.

Mini-Project 4: Modeling Volatility
- Compare the Black-Scholes constant volatility assumption with real market behavior.
- Study the implied volatility (IV) smile and relation with the fat-tailed distributions.
- Implement the GARCH model for conditional volatility.
- Explore the Heston stochastic volatility.