A Comparability Investigation of Numerical Techniques and Scientific Computation for Financial Engineering

This research explores the comparability of various numerical techniques and scientific computing methods applied to financial engineering. Financial engineering relies heavily on advanced mathematical models and computational analysis to value complex financial instruments, manage risk, and optimize investment strategies. This study critically examines the efficiency, accuracy, and computational feasibility of prominent finite difference methods and Monte Carlo simulations. Additionally, it assesses the integration of these methods with modern scientific computing frameworks, to enhance performance and scalability. The investigation includes a series of benchmark tests on common financial problems such as option pricing, portfolio optimization, and risk management. Our findings reveal that while traditional numerical methods like finite differences offer robustness and precision, they often lack scalability compared to Monte Carlo simulations which, despite their computational intensity, benefit significantly from parallelization enhancement. As such, this study gives best practices in selecting and combining numerical techniques and computing frameworks, aiming to equip financial engineers with effective tools for tackling modern financial challenges.