The Monte Carlo simulation is a numerical computing algorithm that computes its outcome through repeated random sampling. It is a technique used to model the different types of uncertainty that impact the value of the investment or underlying instrument under consideration. This study used the Monte Carlo method on a GPU to investigate and assess the Arithmetic Asian Option. By utilizing the GPU's built-in parallelization capability, the study was able to accelerate pricing options more effectively and decisively when compared to the CPU implementation. It also evaluated the amount of power consumed by the GPU and optimized the power for greater efficiency. The effectiveness of the method was examined by utilizing the various paths that were constructed using a randomized function to test this assertion. Ten paths (samples) with ranges between 100,000 and 1,000,000 were taken into consideration. The GPU was utilized to enhance performance in terms of speedup, computation time, power consumption, and time complexity. The GPU's power utilization is then further optimized to improve performance. A detailed experiment using GPU and quad-core multiprocessor systems was conducted. The optimized accelerator for the GPU was coded using the CUDA programming language, libraries, and Application Programming Interface (API). Experimental results using different simulated scenarios demonstrated that the GPU was found to be more efficient in every scenario, both in terms of speed and power consumption. Additionally, the optimized GPU-accelerated optimizer results also showed increased speed and optimally reduced power consumption compared to the quad-core CPU counterpart. This approach will be beneficial in mathematical financial computing and stock market price forecasting.