This report looks into the application of quantum computing in the field of finance, specifically in the pricing of European and American options. Quantum computing, with its unique computational advantage, holds the potential to revolutionise financial modeling in terms of speed and efficiency. The report explores the challenges faced in traditional option pricing strategies and how quantum computing could potentially overcome these limitations. The main focus of the work has been investigating European and American options and their pricing mechanisms. In doing so, it highlights the nature of option pricing, especially for the American ones, which often involves expensive mathematical models and computations.