By the end of the unit, the student should have achieved the following learning goals (LG):
LG1. Know how to specify, estimate, evaluate and interpret econometric models
LG2. Recognize and solve endogeneity problems
LG3. Know and apply panel data models
LG4. Know and apply models with limited dependent variable
LG5. Know how to use econometric packages in data analysis

S1. Linear regression analysis
S2. Nonlinear Regression Analysis
S3. Discrete Choice Models
S4. Models for Continuous Limited Dependent Variables

The final grade will be based on two components: i) two individual problem sets (50%); ii) final (open book) exam (50%). To get approval, students must fulfill the following criteria: i) weighted mean of at least 9,5/20; ii) minimum grade at the exam and each problem set of 7,5/20. There are no re-sitting exams.

Paulo Miguel Grilo da Luz

By the end of this course a student should be able to:
1.1 apply fundamental results of one variable calculus.
1.2 use basic techniques of linear algebra.
1.3 apply fundamental results of vector calculus.
1.4 apply some basic results of measure theory and integration.
The student is also expected to:
2.1 become acquainted with some basic techniques of MATLAB programming.
2.2 be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
2.3 implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Introduction to MATLAB.
II. Sequences and metric spaces.
a) Facts about the real numbers
b) Sequences of real numbers.
c) Metric spaces.
III. Equations in one variable.
(a) Review of single variable calculus
(b) Numerical solutions of equations in one variable:
IV. Systems of linear and non-linear equations
(a) Some basic notions of linear algebra
(b) Direct and iterative methods for solving linear systems.
(c) Review of vector calculus.
(d) Newton's method for systems of (non-linear) equations.
V. Measure, Integration and Probability
(a) Riemann's integral.
(b) Introduction to Measure Theory and the Lebesgue integral.
(c) Applications to Probability theory:

The final grade will be based on homework assignments (50%) and a final exam (50%).
The evaluation of the homework assignments is subjected to oral discussions.
The final exam has a minimum grade of 7.5 out of 20.
Due to the nature of the evaluation in this course, there is no 2nd chance exam.

The main learning objectives of this course are to develop skills to analyse, summarize and to have a critical opinion about the following items: (i) Solow growth model; (ii) neoclassical view of macroeconomics, focused on the notions of general equilibrium, optimizing behaviour, and real cycles; (iii) Keynesian view of macroeconomics, focused on the notions of imperfect competition, price rigidity, and relevance of economic policy; (iv) simulation and estimation of business cycle models.

Dynamic Macroeconomics: Textbook Models
- Solow growth model
- Dynamic stochastic general equilibrium models
- Real business cycle models
- New-Keynesian macro models
- Simulation and estimation of DSGE models

Two moments of evaluation will be considered: an individual assignment (40%) and a written evaluation test (60%). For those who do not undertake the assignment, the written test will be valued in 100%.

By the end of the semester the student should have
developed and be able to apply the following
competences:
A. Knowledge and understanding
- Model the behavior of economic agents;
- Be able to follow the relevant theory regarding these subjects.
B. Application of Knowledge
- Implement theoretical results and modelling
techniques fto perform research;
- Choose the appropriate conceptual, mathematical and graphical approaches to provide solutions for specific problems;
C. Learning
- Development of individual study methods, namely
problem solving and understanding of models and modelling techniques.

1. Consumer theory
2. Producer Theory
3. Markets

Methods of Assessment: Final exam (100%)

José Dias Curto

At the end of this learning unit term, students must be able to:
1. Recognize and apply dynamic models with and without nonstationary variables
2. Recognize and apply conditional heteroskedasticity models
3. Recognize and apply cointegration techniques with and without structural breaks
4. Recognize and apply transition function models
5. Recognize and apply panel data models
6. Work with the R and RStudio econometric/statistical packages
All classes will be held at the computer laboratory

1. Dynamic models, stationarity and unit root
2. Univariate and multivariate GARCH-type models
3. Cointegration, structural breaks and VEC models
4. Threshold models
5. Introduction to panel data models

During the learning-teaching term each student should acquire analytical, information gathering, written and oral communication skills, according to the established learning outcomes for this unit
To contribute to the acquisition of these skills the following learning methodologies (LM) will be used: expositional, active, experimental and self-study

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The evaluation can be done through Periodic Assessment or Assessment by Exam. Evaluation in periodic assessment includes a team work (40%) and a test (60%) covering the entire topics - the score must be at least 7.5 points. In periodic assessment students must attend at least 66.67% of the classes. During the exam students can use all the materials.

This course aims to provide a comprehensive introduction to the pricing of financial assets. We will cover the main pillars of asset pricing, including choice theory, portfolio theory, equilibrium pricing, and arbitrage pricing. Overall, we will opt for breadth of coverage instead of specialization.
Some empirical evidence will also be discussed and there will be exercises with real data. We will learn how to use Excel for empirical work.
At the end of the course, students will be able to read a significant range of current research papers in asset pricing and understand the main issues being discussed.

1. Individual Choice Theory
2. Individual Portfolio Decision
3. Capital Asset Pricing Model
4. Arbitrage Pricing Theory and Factor Models
5. Pricing in Complete Markets
6. Consumption Asset Pricing

o Final Exam: 40%
o Midterm: 30%
o Quizzes, Homework, Class participation, Group presentations: 30%

By the end of this course a student should be able to:
LG1.1 Determine, analytically and numerically, the solution to nonlinear optimization problems.
LG1.2 Determine and analyze, analytically and numerically, the solution to some difference equations.
LG1.3 Determine and analyze, analytically and numerically, the solution to some ordinary differential equations.
LG1.4 Apply algorithms of dynamic programming.

The student is also expected to:
LG2.1 Become acquainted with the basics of programming in MATLAB.
LG2.2 Be able to identify and apply appropriate numerical methods for the analysis of relevant classes of problems arising in economics and finance.
LG2.3 Implement numerical methods in MATLAB and criticize the results obtained from a mathematical, computational and economical/financial view point.

I. Optimization in R^n.
(a) Unconstrained optimization: Necessary and sufficient conditions. Steepest descent. Newton and quasi-Newton methods.
(b) Non-linear constrained optimization: The Karush-Kuhn-Tucker conditions. Penalty methods.

II. Difference equations.
(a) Linear difference equations.
(b) Some notable non-linear equations.
(c) Equilibrium points.
(d) Markov Chains.
(e) Applications: compound interests and gambler's ruin.

III. Ordinary differential equations.
(a) Some notable ODEs.
(b) Existence, uniqueness and qualitative methods.
(c) Euler's method and friends.
(d) Applications: dynamical interest rates, geometric Brownian motion, demographic models and turbulence.

IV. Dynamic programming.
(a) Dynamic programming in discrete time.
(b) Dynamic programming in continuous time.
(c) Optimal control.
(d) Numerical methods.
(e) Applications: modelling sustainable development and money in the utility.

The final grade will be based on 3 homework assignments in groups of 2 or 3 elements (60%) and a final exam (40%) with a minimum grade of 8/20.
Due to the nature of the evaluation in this course, there is no resitting exam.

1. Follow and understand current research topics in the field of Finance.

Attendance of the BRU-IUL and Finance department research seminar series, where papers will be presented in the following topics:
1. Asset Pricing
2. Corporate Finance
3. Derivatives
4. Risk Management

Students must be present at all research seminars. In each seminar students should debate the paper being presented with the presenter. Additionally, at the beginning of each seminar they should turn it a critical summary of the theme being debated. The final grade is the arithmetic average of the grade in these two components.
There is no 2nd chance evaluation.

At the end of the course, the student should be able to:
LG1. Analyse the main theoretical models of mechanism design and auction theory;
LG2. Apply the theoretical concepts to practical applications; and
LG3. Develop a critical assessment of research articles in the area of microeconomics with a focus on topics in mechanism design and auction theory.

P1. Auctions with single unit sale
P2. Mechanism Design
P3. Interdependent values
P4. Multi-unit (identical) auctions
P5. Multiple Object auctions
P6. Applications

The assessment elements and their respective weightings are as follows:
a) 40% presentation of a scientific article (preferably still in an unpublished working paper version) and a peer-review report on the chosen article.
b) 60% final exam (with a minimum mark of 8).

At the end of this learning unit, students should develop a clear and systematic understanding of the main corporate finance theories and their applications:
1. Corporate governance;
2. Asymmetric information, incentives and (financial and economic) distress;
3. Investments, diversification and acquisitions;
4. Capital structure and financing;
5. Payout to shareholders.

1. Introduction to the main corporate finance theories and their applications.
2. Corporate governance.
3. Asymmetric information, incentives and (financial and economic) distress.
4. Investment, diversification and acquisition.
5. Capital structure and financing.
6. Payout to shareholders.
7. Reflection on main corporate finance theories and their applications.

The final grade will be based on three components:
1. Written and oral communication of referee reports on papers related to each of the topics of the syllabus (40%);
2. Written and oral presentation of a literature review (30%);
3. Written and oral presentation of a research project (30%).
Notes:
a. The final grade will be provided after an individual self-assessment report meeting with each student.
b. There is no exam as assessment is based on individual research of the student.

At the end of the course, a successful student should be able to:
1. Knowing how to build an arbitrage strategy with options.
2. Use the main tools of stochastic calculus.
3. Being able to use and derive the Black-Scholes-Merton model.
4. Knowing how to build a dynamic hedging strategy.
5. Being able to implement models with local volatility, stochastic volatility and jumps.
6. Being able to price numerically and analytically American-style options.
7. Being able to price numerically and analytically real options.
8. Being able to price numerically and analytically volatility derivatives.

1. Discrete time theory and martingale pricing

2. Stochastic calculus for finance

3. Black-Scholes-Merton model, the Greeks and the implied volatility surface

4. Local volatility and stochastic volatility models

5. Markovian diffusion processes with killing and Lévy processes

6. American-style options and numerical methods for option pricing

7. Modeling and pricing real options

8. Modeling and pricing volatility derivatives

The final grade will be based on two components:

a) Problem set (50%).
b) Replication project (50%).

1. Understand the econometric methods used in empirical asset pricing
2. Be able to specify and implement empirical asset pricing models

1. Model specification and estimation strategies
2. Affine processes
3. Pricing kernels and factor models

To accomplish the learning goals, the following learning-teaching methodologies (LTM) will be used:
1. Expositional, to the presentation of the theoretical reference frames
2. Showing computer codes for the different models used (Rstudio and Matlab)
3. Active, with the realization of individual works
4. Self-study, related with autonomous work by the student, as is contemplated in the Class Planning.

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The evaluation has two parts. First, the students must carry out an empirical project where they specify and implement an asset pricing model with empirical data. Second, they present an empirical asset pricing paper.

Develop writing and research skills to conduct independent and original research in the field of Finance.

Development of the research project that will form the basis for the student`s dissertation work.

Students must submit a research project containing their proposal for the required three original research papers to be developed during their dissertation.
The report will be reviewed by two faculty members chosen by the Director of the Doctoral Program.
There is no 2nd chance evaluation.

1. Follow and understand current research topics in the field of Finance.

Attendance of the BRU-IUL and Finance department research seminar series, where papers will be presented in the following topics:
1. Asset Pricing
2. Corporate Finance
3. Derivatives
4. Risk Management

Students must be present at all research seminars. In each seminar students should debate the paper being presented with the presenter. Additionally, at the beginning of each seminar they should turn it a critical summary of the theme being debated. The final grade is the arithmetic average of the grade in these two components.
There is no 2nd chance evaluation.

Students who successfully complete this course should be able to:
1. To design, project, adapt and perform original research that meets the requirements of academic quality and integrity and contribute to expand the frontiers of knowledge in Finance;
2. To communicate the results of such research to peers and the academic community in general, including their dissemination through national or international publications with referees.

The nature of the Course does not allow to define a syllabus with concrete subjects.
More important than the transmission of new knowledge, this course aims to apply the skills already acquired to achieve the ultimate goal of completing the thesis. Thus, the syllabus will be set each year based on research projects presented and implemented by the doctoral students, trying to find, through the presentation and discussion of completed or in progress research, the foundations for a better theoretical and empirical contextualization of the student’s work.

At the end of the second and third years a committee will assess the PhD Student/Candidate’s Written Report and its oral presentation, which represents his/her research progress.

The panel members have to write a short justification for the mark they decide to ascribe.

The defense of the thesis is presented when the student and the thesis committee agree that the thesis is essentially completed.