<p>In recent decades, scientific computing has provided a great platform for scrutinizing the complexities of the financial market, particularly for predicting option prices. Forecasting through scientific computing can be achieved based on the market scenarios, which is a dynamic process that allows traders to profit in the finance sector. Hence, we start this article with option pricing models for beginners, having required predefined axioms, their pros and cons, and the available extensions of these problems according to the market situations. We have considered scientific computing as an intersection between interdisciplinary fields- mathematics and computer science; for the present literature on option pricing. The significant contributions of numerical analysis are highlighted even for models within the partial integro-differential equations (PIDEs) framework, too. In general, mathematical models require predefined assumptions in the market, which is hardly available in practice. These assumptions can be relaxed by developing network models through operation research and by machine learning algorithms in a proper scientific way which can differentiate neural nets with respect to the input parameters, to minimize the errors. Here, we provide a detailed scientific analysis of the major machine learning algorithms such as; neural nets, support vector machine, reinforcement learning, etc., and their recent advances with their pros and cons, which are used to handle complex situations, higher dimensional problems, and noise-related issues during data acquisition from financial market with efficient computational costs during training. The state-of-art of the major computational algorithms with recent developments, in the context of option pricing and our present contributions; are also highlighted based on major keywords, through social network analysis between regions all-over the world, and field-wise research contributions from journals on scientific computing.</p>