Course outline

Applied Finance - The course aims to develop the ability to model and price Exotic and interest rates derivatives, applying advanced stochastic methods. Besides the evaluation, the risk management of the derivative portfolio is analyzed. Moreover, some numerical instruments are presented, in particular, Monte Carlo approximation for valuation and applied optimization for calibration. At the end of the course, students should be able to apply the theoretical notions in practical cases by writing effective numerical codes using Matlab or Python.

Economic Models - The course aims at providing some basic knowledge on some fundamental economic models which can be considered as preliminary to further studies in Finance. The course will start from utility theory. Subsequently, the classical mean-variance portfolio selection models will be introduced together with some notions of risk measure. The Capital Asset Pricing Model will be studied and the role of diversification in distinguishing systematic and unsystematic risk will be emphasized. Finally, risk factors will be considered and the Arbitrage Pricing Theory will be illustrated. Some empirical evidence will provide the occasion for a critical view on the models.

Firm Valuation and Capital Market Instruments - The course has the main objective of illustrating the topic of firm valuation. At the end of the course, students will be able to operate the valuation of a firm using the DCF, the income model, market multiples, and EVA. At the same time, students should be able, at the end of the course, to understand the main features of the most important asset classes negotiated in financial markets.

Numerical Optimization and Data Science - The course offers an overview of theoretical and applicative aspects of numerical optimization and data analysis. The main topics are unconstrained nonlinear optimization, simplification and analysis of data in high-dimensional spaces, and machine learning. The aim of the course is to illustrate the main results and to give the possibility of applying the theory to concrete problems using MATLAB.

Quantitative Finance - The course will provide some fundamental notions about the study of quantitative Finance models with a probabilistic approach. Financial markets will be described by the use of probability theory and of stochastic processes. The focus will be the study of European and Exotic options, both in discrete-time models and in the Black and Scholes model.
At the end of the course, students should be able to solve the problems of pricing and hedging European options from a theoretical viewpoint and should be aware of the computational potentialities of this theory.

Probability and Stochastic Processes - This course deals with probability and stochastic processes, having economic and financial applications in view. Accordingly, after introducing some basic notions of probability theory (including conditional expectation), lectures will focus on those processes which are popular in finance. First the discrete time processes are considered, starting from the simple random walk and including martingales, submartingales; then the theory develops the continuous time processes like Poisson process and Brownian motion. Finally we will present Itô integral and basic rules of stochastic calculus.

Real Analysis - The course aims at providing the rigorous mathematical framework needed to understand and use quantitative economic analysis models and computational methods. Specifically, after reviewing the necessary topics of linear algebra and multivariable calculus, the course deals with optimization, measure theory, dynamical systems, and linear partial differential equations.

Statistics for Finance - The course aims to develop the ability to build statistical models for machine learning from financial data.  The presented methods will include generalized linear models, network models, neural networks,    tree models, model evaluation, and comparison.  They will be illustrated by means of practical coding sessions with the R software and with open access data coming from financial markets, credit markets, and payment markets. At the end of the course, students will acquire the skills of a financial data scientist: knowledge of the most important statistical learning methods, capacity to implement them in software algorithms, and ability to interpret the obtained results in financial terms.

Topics in Portfolio Management - The course aims to illustrate the use of some methods and models in order to analyze companies and their functioning, providing rational procedures that allow optimizing investment solutions based on valuation techniques. Students will acquire main concepts that will allow them both to formulate short but comprehensive research and investment cases, according to professional standards generally used in the financial/banking industry, and to manage investments from a portfolio perspective. Particular importance will be given to applications and practical examples, drawn directly from a market context. The training will be completed through the use of common IT tools, showing in detail their use, their potential, and how they can be of support in managing information and data.