The project focuses on model calibration and parameter estimation techniques on real data for GARCH(1,1) volatility model. The GARCH(1,1) model is one of the most popular ways to model time-varying volatility in financial returns. It captures a key property of financial data known as volatility clustering. In this project, we calibrate the parameters so that the model fits real data accurately and we explore how to make calibration faster and more accurate by comparing different optimization methods and computational techniques. We also do hedging using GARCH(1,1) and see the influence of alpha. Further, we also do an advanced python portfolio simulation by simulating a combined portfolio that holds stock in an index fund and also incorporates hedging strategies on options across multiple different stock indexes.