Sidogi, Thendo2014-07-022014-07-022014-07-02http://hdl.handle.net10539/14847In this research report we explore some applications of symmetry methods for boundary value problems in the pricing of barrier options. Various nancial instruments satisfy the Black-Scholes partial di erential equation (pde) but with di erent domain, maturity date and boundary conditions. We nd Lie symmetries that leave the Black-Scholes (pde) invariant and will guarantee that the relevant solutions satisfy the boundary conditions. Using these sym- metries, we can thus generate group-invariant solutions to the boundary value problem.enSymmetry groups.Differential equations, Partial.Boundary value problems.Thesis