Gumbo, Mukudzeyi M2019-05-292019-05-292018https://hdl.handle.net/10539/27321dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. June 17, 2018One of the fundamental assumptions of the classical Black-Scholes model is that of constant interest rates through the life of a derivative instrument until expiry. While this assumption greatly simpli es the pricing of derivative instruments it also results in an inherent aw of the model as interest rates tend to uctuate over time depending on the economic environment and how market players perceive the future economic environment to be like. This dissertation focuses on a Black-Scholes model in which the constant interest rates assumption is relaxed, i.e. interest rates driven by time-dependent stochastic processes. Lie theory and invariant approaches will be utilized to nd solutions of this model, whose derivation shall also presented in this dissertation.enThesis