This final project focused on the GARCH(1,1) model for stock path modeling, as well as methods for visualizing and comparing different stock path models.
The GARCH(1,1) (Generalized AutoRegressive Conditional Heteroskedasticity) model is a stochastic volatility model which is used to model stock paths. The model introduces autocorrelation features to volatilities, similar to the Heston model. In visualizing these models, we were motivated by the observation that noise obscures much of the differences between different stock path models. Our approach to this problem involves generating stock paths across three models (Geometric Brownian Motion, Heston, and GARCH(1,1)) using the same noise functions. We also used the same approach to visualize the profits of a delta-hedged portfolio.