This course is an introduction to mathematical finance, i.e. to fundamental concepts and models in quantitative finance, as well as to financial mathematics, i.e. the mathematics used in
quantitative finance and quantitative risk management. We will also discuss how these models are implemented in practice (numerical implementation, calibration). Although the primary
focus of this course is theoretical, it is essential to grasp how these concepts translate into code when used in practice.
The different chapters of the course relate to risk, arbitrage, discrete-time models, Brownian motion, stochastic calculus, PDE approach, risk-neutrality and martingale measures, change of numeraire, local volatility, stochastic volatility and energy derivatives.