The program aims both to provide a current and solid theoretical base and to develop the analytical skills needed for practical work and research. In this way, students are familiarized with the design, analysis, and empirical comparison of theoretical models. The study of mathematical and econometric techniques will allow students to undertake their work with the necessary rigor.
The aim of this course is to fully cover the main concepts and techniques of mathematical analysis, probability and statistics that will be required for the rest of the Master's Program. The course begins with an analysis of sets and functions. The next step is the study of differential equations, particularly regarding the existence of a solution and its global and local stability. In addition, the course addresses some aspects of the theory of probability and statistics such as sample spaces, random variables and moment generating functions. Finally, some stochastic processes of particular interest are covered, such as Poisson's processes and Markov chains.
The class focuses on developing and understanding the main ideas and techniques necessary for the analysis of general equilibrium models. It begins by analyzing the basic general equilibrium model through the identification of its properties. The course continues with the study of the repercussions of externalities and public goods on the equilibrium. The module is completed with the study of three specific topics: the existence and uniqueness of equilibrium, general equilibrium under uncertainty, and the dynamic general equilibrium model
The course offers an overview of major topics in modern macroeconomics and dynamic analysis. The objective of the course is twofold. On one side, it focuses on the main intuition behind each economic question and theoretical model. On the other side, students will get acquainted with the techniques of dynamic macroeconomics. Using these techniques, the course introduces students to the analysis of intertemporal consumption choices, economic growth and business cycle fluctuations, with various applications. This program is meant to improve students' understanding of economic phenomena and their preparation for the following course on monetary and open-economy macroeconomics.
This course provides the student with a basic understanding of the building blocks of Industrial Organization models. The basic purpose is to familiarize the student with the modelling tools that are commonly used in modern Industrial Organization analysis. Specifically, the course focuses on the study of Monopoly, Game Theory, and Oligopoly, leaving some time to deal with some selected topics such as product differentiation and vertical relations.
The objective of the course is to familiarize students with the adequate tools to use econometric techniques appropriately. The course includes rigorous treatment of the classical linear regression model, maximum likelihood estimation, asymptotic theory, nonlinear regression models, generalized method of moments, time series, including advanced topics such as nonstationary and long memory processes.
This course intends to make the student familiar with basic statistical and econometric techniques that are used in the analysis of microeconomic data. The course covers both the theoretical and the applied aspects of these techniques, including estimation of models by the general method of moments, treatment of endogenous regressors, linear methods for panel data models, and limited dependent variable models.
This course is an introduction to modern financial theory. It focuses on the basic theory of interest rates and fixed income securities, and explicitly examines the term structure of interest rates. It also reviews the applications to capital budgeting, optimal bond portfolios and the valuation of the firm. The course also focuses on the CAPM and factor models. It ends with an introduction to arbitrage pricing theory and risk neutral pricing for one time period market models.
This module starts with analysis of forwards, futures and swaps. It examines the concepts of conditional expectations, martingales and the Central Limit Theorem. It continues with the study of multiperiodic market models and the fundamental theorems of asset pricing. The CRR model for European type options and the Black-Scholes formula as limit to the CRR model follow. The module ends with the "Greeks" and their application to hedging.
The course is intended to provide participants with the necessary tools to apply state of the art techniques for the forecasting of financial and macroeconomic variables and turning points, with special emphasis on recent developments in "nowcasting" The course covers the required financial and econometric theory but with the intention of putting it into practice in specific forecasting situations. Studens will receive computer codes that exactly match the techniques covered in class in order to guarantee their applicability to real data.
Throughout the year, students must attend and actively participate to the weekly Research Seminars organized by the School of Economics and Business Administration. Seminars are usually held by invited researchers (from other Spanish institutions or from foreign institutions). Internal seminars are also possible.
The research project consists on the elaboration of an original research paper on a topic related to one of the subjects studied during the program. It should represent a significant contribution to the subject from a theoretical or empirical point of view, and be of sufficient quality to be published in a scientific journal. This project will be supervised by at least one member of the faculty and will be graded by a board of examiners.