زينب شبر

This thesis focuses on employing a modern numerical technique to solve the Black-Scholes partial differential equation, widely utilized for pricing financial options, through a mesh-free method based on radial basis functions. Traditionally, such equations are addressed using standard numerical approaches, including finite differences, finite elements, or finite volumes. Additionally, option pricing can also be achieved using binomial models or Monte Carlo simulations. The Radial Basis Point Interpolation (RBPI) method proves particularly advantageous for cases involving higher-order derivatives, such as in basket options, where the payoff depends on the value of a portfolio (or basket) of derivatives. This approach enables the concentration of computational efforts and degrees of freedom in the most critical regions of the domain, optimizing resource allocation. This work demonstrates the application of radial basis point interpolation to several test problems and eva‎luates the convergence of discrete solutions to exact ones, along with an analysis of computational efficiency. The findings confirm the validity of the method and the consistency of the results obtained. Future work will explore its application to problems in higher dimensions and the potential for parallel computing implementations.

قيمت‌گذاري اختيار , روش‌هاي تابع پايه شعاعي , معادله بلك-شولز , تكنيك‌هاي عددي

Option Pricing , Radial Basis Function Methods , Black-Scholes Equation , Numerical Technique

Zainab Shubbar

Mahboubeh Molavi-Arabshahi