Solving a partial differential equation associated with the pricing of power options with time-dependent parameters

Previous analysis and research on the power option - one of the exotic options - have focused on the interest rate of the stock and its volatility as constant parameters throughout the run of execution. In this paper, we attempt to extend these results to the more practical and realistic case of when these parameters are time dependent. By making no ansatz or relying on ad hoc methods, we are able to achieve this via an algorithmic method - the Lie group approach - leading to exact solutions for the power option problem.