This submission comprises four mini-projects. In the first two mini-projects, I analyzed stock data over the last three years for the United States's three major legacy airlines (American (AAL), Delta (DAL), United (UAL)). The first mini-project involved analyzing risk and reward (mean and variance) for each airline and providing examples of high- and low-risk investment strategies. The second mini-project involved comparing the airline log-returns to normal distributions, over 3-month intervals, and identifying seasonal patterns in airline behavior. The third mini-project involved graphing the rate of change of the Black-Scholes call and put options as time and spot price varied. The fourth mini-project involved using the Heston model equation to generate a stream of variable volatilities, thereby improving the Black-Scholes equation for stock prediction with sigma-hedging; 10 different stock graphs were created.

https://github.com/mathbird7283/quantfinance2025-final-project