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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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This course will provide the tools to analyze macroeconomic policies and the international transmission of economic fluctuations in open economies. The course is divided into two parts. The first part studies monetary policy models. It starts with a brief introduction on the state of macroeconomics after the Great Recession. It continues with an analysis of the Lucas’ Island Model, dynamic inconsistency issues and the optimal choice of policy instruments. The next step is the study of the New Keynesian model and of the current directions of research. The second part of the course provides an introduction to open economy models. Topics include (i) the role of different exchange rate polices for monetary and fiscal policy in a small open economy; (ii) international real business cycle theory; (iii) currency crises models.

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Asset managers need to understand how their clients think. In recent decades discoveries about how humans judge and decide helped to enrich traditional models of the rational, self-interested decision-maker. Researchers started to examine cognitive limitations, social aspects of decision-making, and the impact of emotion in financial decisions.

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This course aims to present a comprehensive review of the methods used to evaluate social policy, focusing in evaluations in the developing world to the student. We study he theory of different methods focusing on the discussions of identification and estimation. Additionally, we explore the main challenges throughout the process of implementing an evaluation.

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The subject Research Seminars consists of three parts I, II and III, in line with the annual academic schedule: part I from September to December, part II from January to March, and part III from April to June. Each students has to present two seminal papers along the academic year in order to lead the student to the research frontier in a particular field of Economics or Finance. Ideally, the papers chosen by the student are related to his/her Master Thesis. Like this the student acquires presentation and communication skills apart from developing his/her critical thinking. Attending research seminars is compulsory for students. They sould see it as an opportunity to get acquainted to ongoing research. Seminars are usually held by invited researchers (from other Spanish institutions or from foreign institutions). Internal seminars are also possible.

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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.

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