Wafo, Soh, Celestin2019-07-102019-07-101997https://hdl.handle.net/10539/27607A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science.A Lie group assisted method is used to solve explicitly an arbitrary initial value problem for the Black-Scholes equation, This equation plays a crucial role in the mathematics of finance. It was first solved by its inventors for a special initial data. Our solution generalises the well-known Black-Scholes formula.enLie groups.Cauchy problem.Differential equations, Partial.Mathematical models.Business mathematics.Thesis