Cálculo Estocástico e Integración Numérica: Valoración de Opciones Europeas

Abstract

This Final Degree Project explores key techniques for the valuation of financial options: the BlackScholes method and Numerical Integration. The objective is to conduct a detailed analysis of the theoretical foundations and apply both methodologies in the valuation of a real portfolio of European options. The study delves into stochastic calculus, deriving the stochastic Black-Scholes formula, and addresses numerical integration with emphasis on Euler-Maruyama and Milstein methods, supported by Monte Carlo simulations. The development of both techniques is carried out through literature review, theoretical and empirical analysis, utilizing data from public sources, and Python programming.