CEMLA Course: Financial Mathematics (introductory)

The online sessions of the Financial Mathematics course were designed to provide a solid introduction to the theoretical foundations of quantitative finance. Throughout these sessions, the historical development of the discipline was presented, from early random walk models to modern derivative pricing theory, highlighting the contributions of Bachelier, Einstein, Wiener, Itô, and the central role of the Black–Scholes model.

The course covered the essential concepts of stochastic calculus, including Brownian motion, martingales, and stochastic differential equations, as well as the Feynman–Kac theorem, which links stochastic processes to partial differential equations. These results allowed for the introduction of risk-neutral valuation and the economic interpretation of the Black–Scholes formula, laying the conceptual groundwork for modern option pricing.