The fundamental aim of this proposal is to establish some basic concepts for the underlying asset, including some basic computational tools. In most cases, however, there is no empirical solution for such problems as option pricing, so there are some numerical methods that have mentioned below to find approximation; the Binomial tree method, finite difference method, and Monte Carlo simulation. First of all, for almost every form, an algorithm was written based on Hull and Wilmott for this type of problem. After that, these algorithms can be enhanced as needed in certain ways. For example, Both the speed and memory use of the binomial tree variables are often increased by using just one vector instead of modifying the entire price storage matrix. Computational time is minimized in Monto Carlo simulations by introducing a parallel algorithm capable of enhancing velocity by a factor, equal to the number of processors used. By applying the different methods, for European and PSX, to the same problem, I will measure the solution of the problem and eventually compare the results and explain which method is faster and more accurate. The preliminary data set collected from the region around Kathmandu Valley and the main lines of the country can map some interesting features and environmental proxies that are visualized and the patterns and variations in it are explored using different models such as Autoregressive Integrated Moving Average (ARIMA), Recurrent Neural Network (ARIMA), Recurrent Neural Network.