Pricing of double barrier options from a symmetry group approach

Abstract

In 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.