Abstract - Options are imperative, yet complex instruments in financial markets, primarily deployed to hedge, manage risk and speculation. Pricing these instruments to near accuracy is critical for its use as mispricing can lead to unethical speculation and arbitrage, not to mention financial risk. Since the development of closed form models, numerous analytical, simulation, machine learning and stochastic approaches have been calibrated to improve valuations and address assumptions which may not align to the real world. This paper presents a comprehensive review of pricing strategies; stemming from options and payoff fundamentals, then into exploring various traditional plus algorithmic methods addressing volatility in pricing, and buttressing the theoretical review with computational experiments, with payoff visualizations, and pricing simulations. The objective of the study is to emphasize the advantages and constraints of various option pricing strategies, with an emphasis on their transdisciplinary significance in the fields of computational finance, risk management and applied mathematics. Key Words: option pricing, derivatives, Black-Scholes, Numerical Methods, quantitative finance
R et al. (Sun,) studied this question.