At first basic quantitative tools are introduced in order to approach quantitative finance. In particular functions in several variables are presented.
Modern finance is today an extremely rich field and often uses complex mathematical tools.
The main purpose of the first part of the course is to present the main topics of quantitative finance in a clear and accessible way with the aim to stimulate intuition without abandoning the aspects of formalization that are now indispensable for anyone wishing to operate on financial markets.
The second part of the Course aims to provide an overview on the most recent valuation models of financial stocks and derivatives. Starting from the axiomatic foundations, it analyzes the market with the intention of showing students how to formalize some financial phenomena.
The course has as main objective the study of the main methods for the numerical approximation of partial differential equations and stochastic differential equations.
In particular, we will analyze the main differential models for the evaluation of financial securities and derivatives. You will have several hours of computer lab, during which students can experience the main theoretical concepts presented and deepen their understanding and use through the development of application programs that use the software Matlab.
At the end of the course, the student should:
- understand and properly treat the main models presented in the course;
- be able to solve practical problems (exercises and software applications);
- show good skills in making judgement;
- clearly communicate what he/she has learned.