Investors utilize the pricing of financial derivatives to enhance expected returns and mitigate risks associated with their portfolios. Among these derivatives, options are particularly valued for their potential to offer limited downside risk while allowing significant upside potential. Accurate pricing of options is therefore crucial for both theoretical and practical purposes, driving ongoing research in the development and refinement of pricing models. In this paper, we examine the well-established binomial and trinomial lattice models for option pricing, which are widely used due to their flexibility and ease of implementation. We focus on the binomial method, and present several key optimizations aimed at improving computational speed and reducing memory usage in the implementation. These enhancements are crucial for handling large datasets and real-time pricing in high-frequency trading environments. Additionally, we explore modifications to the binomial model that make it more suitable for pricing American options, which require the consideration of early exercise features. The trinomial model is also considered as a natural extension of the binomial approach, offering potential benefits in terms of accuracy and convergence. Through a series of MATLAB simulations, we compare the performance of these models, both in their standard forms and with the proposed optimizations. The results highlight the trade-offs between computational efficiency and pricing accuracy, providing insights into the practical application of these lattice-based methods in various financial contexts. Our findings contribute to the ongoing development of more efficient and accurate tools for option pricing, which are essential for both academic research and the financial industry.