Kometsi, Relebohile Veronecca2025-11-062025-11-062025-07https://hdl.handle.net/20.500.14155/2225Honours' degree thesisThis project aims to solve the barrier options model with linear time-dependent volatility, described as a Partial Differential Equation (PDE) using symmetry analysis. The only PDE to be considered will be the Black-Scholes model. Firstly, we use Lie symmetry to find symmetries of our model from our determining equations. Once the symmetries are found, they will b e picked at random to form characteristic equations needed to find invariant solutions. Lastly, the solutions will b e interpreted and graphed.enThesis