This course is an introduction to concepts and models used in quantitative finance, presented in the framework of derivative pricing theory. At the same time, this course introduces a branch of mathematics, stochastic calculus, which is the cornerstone of derivative pricing theory. It will also discuss how the models are implemented in practice via their numerical implementation and calibration. Although the primary focus of the course is theoretical, it is essential for the students to grasp how all the concepts translate into code for practical implementations.
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 and one or two more advanced topics, like local volatility or least-square Monte Carlo methods.