# Master Economics # Quantitative finance and insurance

## RESPONSABLES

## AIM

The training provides a comprehensive approach to insurance and financial markets. It gives students both empirical and theoretical skills which allow them to specifically understand market mechanisms. The main goal is to provide the student with a certain number of theoretical and empirical tools to allow him/her to evolve in most jobs of the financial and actuarial sector and to grasp the future stakes. This track is co-organized with Centrale Marseille. The majority of courses specific to this track are common to both schools.

## LINKS WITH RESEARCH

This Master’s degree is part of the *Ecole Universitaire de Recherche (EUR) AMSE*, which gathers together almost a hundred researchers from AMU, CNRS, EHESS, and ECM.

The teachers are selected according to their expertise within those institutions. The teaching staff is supplemented with practitioners.

## FUNDAMENTAL PREREQUISITES

Solid bases in microeconomics (especially contract theories), as well as probabilities (conditional probabilities among others) and statistics (estimating and testing) are necessary. Notions in economics of uncertainty are recommended.

## RECOMMENDED PREREQUISITES

This track is particularly adapted to students who have validated the first year of the Master of economics in the AMSE department of the Faculty of Economics and Management of Aix-Marseille University. Access is possible in second year (M2).

## WEB SITE

## PLAQUETTE DE LA FORMATION

## PROFESSIONAL SKILLS

Main professional skills targeted at after graduation :

- To understand how insurance and finance markets work.
- To apprehend and model financial and insurance related settings to build relevant strategies.
- To evaluate a company or project with a view to funding or to deal
- To evaluate a financial asset prior to positioning (buying/selling)
- To compare various investment strategies
- To measure the performance of financial assets
- To modelize behaviour in the face of risk
- To solve complex financial problems

## INTERNSHIPS AND SUPERVISED PROJECTS

At the end of the year, the students go through an internship and write a master’s internship report . The goal of the report is to prove their ability to apply the conceptual tools they have acquired to issues of the professional world. The student must therefore identify the question, implement the tools and be able to communicate the results to a professional audience as well as an academic one. The project is tutored by a scholar and an internship director (a member of the business). The report is defended in front of a jury comprised of the academic tutor, the internship director and two other people with acknowledged skills (and at least one scholar).

## PLAQUETTE DE LA FORMATION

## EVALUATION AND EXAMS

Each course is assessed by a written exam or the making of a file presented during an oral defense. In order to limit the number of personal projects for each student, the teachers propose transversal projects when that is possible.

### Track FQA (OPPT) (120 ECTS)

### M1 Economics (AN) (60 ECTS)

### S1 M1 ECO (SE) (30 ECTS)

### Microeconomics I and II (6 ECTS)

### Microeconomics I

## CONTENT

The objective of this course is to provide students with the foundations of economic theory. The course covers the consumption and production theory and is textbook based. The difficulty and coverage compare to those of the main departments of economics worldwide.

__Course outline :__

The course is textbook based. Topic list : Technology, Profit Maximization, Profit Function, Cost minimization, Cost Function, Duality, Utility Maximization, Choice, Demand.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Microeconomics II

## CONTENT

The objective of this course is to provide students with the foundations of economic theory. The course covers the consumption and production theory and is textbook based. The difficulty and coverage compare to those of the main departments of economics worldwide.

**Course outline :**

The course is textbook based. Topics list : Exchange, Time, Equilibrium Analysis, Welfare.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics I and II (6 ECTS)

### Macroeconomics I

## CONTENT

Learn the basic models with microeconomic foundations used in modern macroeconomics. Be able to do dynamic analysis. Understand the concept of dynamic efficiency and the role of public expenditures.

**Course outline :**

1. Introduction with reminders on the Solow model

2. The Ramsey model

2.1. The framework

2.2. Existence and features of the steady state

2.3. Dynamic analysis

2.4. Extension : public spending

3. The overlapping generations model

3.1. The model with capital

3.2. Intertemporal equilibrium, steady states and dynamics

3.3. Optimality

3.4. Extensions : public spending ; rational bubbles

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics II

## CONTENT

The aim of the course is to present advanced macroeconomic topics related to the analysis of aggregate consumption, aggregate investment and modern business cycle analysis with the Real Business Cycle model.

**Course outline :**

Chap. I : Consumption theory

1. Consumption over the life cycle : the life-cycle/permanent income models

2. Introducing uncertainty – The random walk hypothesis

3. Market imperfections : the role of liquidity constraints

4. Extensions : risk aversion, precautionary savings

Chap. 2 : Investment theory

1. The neoclassical model of capital demand

2. Investment with and without capital adjustment costs : Q-theory models

3. Role of shocks : real shocks, news shocks, noise shocks

Chap. 3 : Real Business Cycles

1. Measuring business cycles : trend-cycle decompositions and stylized facts

2. The canonical RBC model

3. Evaluation of the model

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics I and II (6 ECTS)

### Econometrics I: linear model

## CONTENT

**Provide students with :**

- the basics of panel data econometrics (fixed effects models, error components model)
- the identification of endogeneity problems in econometric models and their treatment (instrumental variables, GMM, tests)

**Course outline :**

1. Introduction to panel data and panel data models

2. The fixed effects model

- Specification of the model
- Estimation of the model : the Within / LSDV estimator.
- Testing the absence of unobserved heterogeneity.

3. The error components model

- Specification of the model
- Estimation of the model : the GLS / FGLS estimators.
- Testing the absence of unobserved heterogeneity.
- Testing the absence of correlation of the effects : the Hausman test

4. Endogeneity issues

- Causes of endogeneity in econometric models : measurement errors, dynamic models, unobserved heterogeneity, etc.
- The instrumental variables estimator
- The GMM estimator
- Looking for instruments (the time-series case, the cross-section case, the panel data case).
- Testing the validity of instruments
- Testing the exogeneity of regressors

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics II: non linear model

## CONTENT

Provide students with the basics of the econometrics of non linear models for binary, multinomial, ordered and count dependent variables as well as models for censored and truncated variables.

**Course outline :**

1. Introduction to non-linear models in econometrics and a brief reminder about the maximum likelihood principle.

2. Models for binary dependent variables.

- The linear probability model.
- The Logit model.
- The Probit model.

3. Models for multinomial and ordered dependent variables.

4. Models for count data.

5. Models for truncated and censored variables.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Labor economics - Risk and incentives (6 ECTS)

### Labor economics

## CONTENT

The objective of this course is to provide students with the necessary analytical tools to be able to study the consequences of different institutions, human capital formation, discrimination and wage bargaining on the labor market.

**Course outline :**

Introductory Chapter :

- Presentation
- Objectives
- Evaluation
- Labor market Institutions and course outline

Chapter 1 : « Labor Supply and Labor Demand » :

- Key definitions
- Labor Supply
- Labor Demand
- Equilibrium

Chapter 2. « Minimun wage »

- Facts
- Classical analysis
- The monopsony case
- Dual labor markets

Chapter 3 : « Mandatory contributions and social benefits »

- Facts
- Classical analysis
- Accounting for wage rigidities

Chapter 4. « Labor Unions » :

- Facts : unions, collective bargaining, union density
- The objective of labor unions
- Models of collective bargaining
- Model of strikes
- Empirical evidence and policy issues

Chapter 5. « Discrimination » :

- Facts : gender and ethnic wage and employment gaps
- Economic theories on discrimination
- Measuring wage discrimination
- Empirical results in the literature and policy issues

Chapter 6. « Education and human capital formation » :

- Facts
- The theory of human capital
- Education as a signaling device
- Identifying the causal relation between education and income
- Returns to education : private vs social returns

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Risk and incentives

## CONTENT

The main objective of this course is to provide the students with a theoretical synthetic framework so that they can face the difficulties of the study of economic decisions under uncertainty. Two main general topics will be dealt with : (1) the theory of decision under uncertainty, and (2) the moral hazard issues between several economic agents.

**Course outline :**

Chapter 1 : Risk, uncertainty and strategies

- Introduction of the main concepts (risk, uncertainty, probability, moral hazard, adverse selection)
- Probabilistic framework (space of states, random variables)
- Numerical decision criteria (preferences, representation by a numerical criteria)
- Game theory, Principal-Agent model

Chapter 2 : Expected Utility

- The virtues of the expected utility (Saint-Petersburg paradox)
- The axiomatics of the expected utility (objective and subjective expected utility)
- The limits of the expected utility (Allais paradox, Ellsberg paradox)
- Generalisations of the expected utility (rank-dependent expected utility, Choquet expected utility)

Chapter 3 : Risk Aversion and Risk Measures

- Qualitative approach (certainty equivalent, risk premium, risk attitude)
- Quantitative approach (local measures of risk aversion)
- Stochastic dominance (first and second order)

Chapter 4 : Introduction to moral hazard issues

- Risk sharing and sharecropping contracts
- Credit with risk aversion of the borrower

Chapter 5 : Other applications

- Risky saving
- Application of the expected utility to static portfolio choice

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Methodology I (6 ECTS)

### Software for economists I

## CONTENT

Provide students with the basics of the statistical and econometric treatment of data using SAS, from the statistical description of the sample, the detection of outliers to the implementation of estimation techniques for linear and non-linear models.

**Course outline :**

1. Introduction to SAS : importing and managing data – proc import, proc contents, proc format, proc sort, proc surveyselect and introduction to SAS macro functions.

2. Describing the data : descriptive statistics with SAS – proc means, proc univariate, proc freq, proc tabulate, proc gplot.

3. Estimating and testing linear models : proc reg, proc glm, proc model, proc panel.

4. Estimating and testing non linear models : proc logistic, proc probit, proc model, proc genmod, proc nlmixed.

## VOLUME OF TEACHINGS

- Tutorials:
**24**hours

### Mathematics for economists

## CONTENT

The course intends to deepen the understanding of optimization theory with a geometric approach, and to introduce in a second part the study of dynamical systems.

__Course outline__

**I. Optimization with mixed constraints** a. Tangent cone and KKT conditions b. Mixed constraints problem c. Constraints qualification conditions d. Convex problems e. Saddle point and duality

II. **Dynamical systems** a. Introduction b. Systems of linear equations

- Constant coefficient : resolution, exponantial of matrices
- Dynamic of the solutions : steady state, stability, planar systems
- nonhomogeneous systems c. Systems of nonlinear differential equations
- Existence and uniqueness theorem
- Linearized system, Hartman-Grobman theorem

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Elective course, choose one among two

### Refresher course in economics (0 ECTS)

## CONTENT

For students coming from other fields than economics : quick reminder about the fundamentals of Economics : utility and profit maximization, optimization, markets, equilibrium

**Course outline :**

1. Principles and key concepts of Economics

2. Foundations of Microeconomics : consumer decision and utility maximization

3. Foundations of Microeconomics : producer profit maximization and market equilibrium under perfect competition

## VOLUME OF TEACHINGS

- Lectures:
**6**hours

### Refresher course in mathematics and statistics (0 ECTS)

## CONTENT

For students who want to improve their math level : reminder about prerequisites for the Mathematics classes and basic notions of probability and statistics.

__Course outline :__

1. Linear algebra

2. Analysis and optimization

3. Matrix diagonalization

4. Ordinary differential equations of order 1

5. Basic notions of probability and statistics

## VOLUME OF TEACHINGS

- Lectures:
**6**hours

### S2 M1 ECO (SE) (30 ECTS)

### Microeconomics III and IV (6 ECTS)

### Microeconomics III - Game theory

## CONTENT

Introducing the basic concepts of Game Theory.

**Course outline :**

1. Complete information games (normal form, examples, analysis)

2. Mixed extension (lotteries, expected gain, mixed-strategy equilibrium)

3. Games with continuous actions (externalities,imperfect competition)

4. Incomplete information games (extensive form, subgame perfection)

5. Additional examples.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Microeconomics IV - Public economics

## CONTENT

The objective of this course is to study the role of state in the economy. It is designed to provide students with a broad overview of issues investigated in public economics. We will review the rational foundations of public intervention and explore some of the tools used by government to act : taxes and transfers, the provision of public goods, or the design of welfare schemes. Most topics will be approached from both theoretical and empirical points of view.

__Course outline :__

**Lecture 1 – Introduction to public economics**

- Foundations of public intervention – Normative and positive public economics – Some numbers about public intervention – Empirical methods for public economics

**Lecture 2 – Social choice and social welfare**

- Axiomatic approach to social choice – Social welfare functions

**Lecture 3 – Public goods and externalities**

- Public goods – Externalities

**Lecture 4 – Taxation of commodities**

- Tax incidence – Optimal commodity taxation

**Lecture 5 – Taxation of labor**

- Optimal labor taxation – Some empirics around labor taxation

**Lecture 6 – Taxation of capital**

- Taxes in an intertemporal framework – Optimal capital income taxation – Taxation of inheritances

**Lecture 7 – Social insurance**

- Unemployment insurance and workers’ compensation – Disability insurance – Health insurance

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics III and IV (6 ECTS)

### Macroeconomics III

## CONTENT

This course follows Macroeconomics II and it goes deeper in the description of micro-founded models by introducing market frictions into the RBC model. The DSGE-New Keynesian model which includes nominal rigidity is a natural extension of the RBC model to analyze monetary policy / fiscal policy. Although this course is mainly theoretical, lectures will be motivated by stylized facts and the empirical performance of business cycle models will be discussed.

**Course outline :**

Chapter 1 : Nominal rigidities (1) Introducing money in RBC model (2) Monopolistic competition (3) Price rigidity (4) Exercises

Chapter 2 : Monetary and Fiscal policy (1) Monetary policy analysis (2) Fiscal policy analysis (3) New topics in macroeconomics (ZLB, forward guidance…)

(4) Exercises

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics IV

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Methodology II (10 ECTS)

### Time series

## CONTENT

This course develops the basic theoretical tools for the analysis and estimation of univariate time series models. In particular, it discusses the concepts of stationarity and non-tationarity, unit-root tests, and exposes the techniques for estimating, forecasting and testing ARMA models using practical examples. Finally, it presents some non-linear models for conditional mean and variance.

**Course outline :**

• Brief Review of Statistics and Probability Concepts (pre-requisites)

• Stochastic processes and stationarity

• Classical stationary processes : AR, MA, ARMA

• Estimations techniques for the classical processes

• Forecasting methods for ARMA(p,q) processes

• White noise tests and stability tests

• Optimal choice of orders and Adequacy of parameters

• Univariate Non-Stationary processes and cointegration

• Modelling Nonlinearity of the conditional expectation

• Volatility modelling for univariate processes

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Software for economists II

## CONTENT

The objective of this course is twofold. Firstly, to study how to use and manipulate databases with Stata and secondly, to perform empirical analysis in relation with the concepts learned in the time series and econometric methods of evaluation classes. After a short introduction to Stata, the course will be divided into tasks-oriented sessions (with mini-projects and exercises) during which the students will perform empirical analysis using databases such as the World Values Survey, the French Labor Force Survey, the National Supported Work data, etc.

**Course outline :**

Lecture 1 : Introduction to Stata and database manipulation

Why using Stata – What Stata looks like – Importing and reading data into Stata – Examining the data – Saving the dataset – Keeping track of things – Organizing datasets – Creating new variables – Panel data manipulation

Lecture 2 : Graphs and linear regressions

Histograms – Two-dimensional graphs – Linear regressions – Post-estimation – Extracting results – Hypothesis testing – Interaction terms – Non-linearity – Fixed effects

Lecture 3 : Endogeneity and public policies econometrics

Randomized control trials – Difference-in-differences – Validity checks

Lecture 4 : Time series

Stationary and non-stationary processes

## VOLUME OF TEACHINGS

- Tutorials:
**24**hours

### Mathematics for finance

## CONTENT

**Objectives :**

Introducing elementary tools to analyse discrete and continuous-time random processes.

**Roadmap :**

1. Markov chains

1.1. Introductory Example : random walks

1.2. Markov chains on a finite state space

1.3. Markov chains on countable state spaces

1.3.1. States classification

1.3.2. Asymptotic results

2. Markovian processes in continuous time

2.1. Poisson processes

2.2. Continuous-time Markov processes

2.3. Queueing theory

3. Discrete-time random processes

3.1. Conditional expectation

3.2. Martingales

3.3. Stopping time

3.4. Convergence theorems

3.5. Applications

4. Introduction to continuous-time stochastic processes : Brownian motion

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Evaluation by econometric methods

## CONTENT

The objective of the course is to offer M1 students with an overview of the main empirical methods used for the evaluation of public policies. We will study key articles taken from various applied economics literature (health, education or activive labor policies). Practical case studies on STATA will be offered all along. We will point out advantages and limits of each method as well as guide in the selection of the appropriate method.

**Course outline :**

Introduction

1. Why evaluate ? What do we evaluate ? What is the objective ?

2. Potential outcome framework

3. Treatment effects and counterfactuals

4. Selection bias

Chapter 1 : Randomized experiments

1. Random assignment

2. Underlying assumptions

3. Study of 2 empirical papers using the method

4. Randomized experiments in practice

Running example : exercise on National Supported Work (NSW) data

Chapter 2 : Natural experiment : Difference-in-difference method

1. Model and underlying assumptions

2. Study of 2 empirical papers using the method

3. Extensions

4. D-in-D in practice

Running example : exercise on National Supported Work (NSW) data

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Elective teaching unit, choose 2 among 3 (8 ECTS)

### Project management - Health and environmental economics (4 ECTS)

### Project management

## CONTENT

Designing and managing development aid projects according to international standards.

**Course outline :**

The students will learn and practice how to build a development program.

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Health and environmental economics

## CONTENT

The goal of this course is to bring together health and environmental economics as two narrow fields within the discipline of economics. This shall be done by identifying the interactions and intersections between health and environmental issues, describing the main economic properties that health and environment do have in common (market failure, externalities, government involvements …). This shall be followed by delineating the unique features of health and environment that make of them two distinct topics of study. Following this line of reasoning, the course shall, then, present two self-contained parts devoted to health economics and environmental economics. Each part shall present the workhorse analytical concepts and methods used by economists to explore specific issues relating to the two subfields. The course shall emphasize the use of economic evidence to identify priority issues and the most effective policies for health and environment. Examples and experiences of the kinds of topics that are addressed shall be provided all through the course.

**Course outline :**

Part I (4 hours) Overview : The links between health, environment and the economy

• Economic properties of health and environment

- What distinguishes “health goods” from “environmental goods” ?
- Typology of goods : Pure vs. impure public goods, private vs. publicly-provided private good, global vs. local public goods.

• The economic valuation approach :

- The theory of externalities
- Welfarism vs. extra-welfarism analysis
- Cost-benefit analysis, cost-effectiveness analysis, cost-utility analysis.
- Revealed vs. stated-preferences methods

• Government intervention and regulations

- Why do governments provide goods that are not pure public goods ? The case of health care services.
- What are the special characteristics and challenges of the “global public goods” ? The case of global climate change
- Rationing devices for publicly-provided goods (User charges, uniform provision, queuing).
- Efficiency conditions for public and pure public goods : Collective demand curve and provision of public goods.

Part II (7 hours) : Economics of Health and Health Care

• Overview : Health economics as a field of inquiry

• Health care market structure, conduct and performance :

- Do the law of supply and demand apply to health and health care ?
- What makes health and health care different ?
- Demand for health and health care : Health behavior
- Supply of health care : Production, provision and costs of health care.
- Health insurance markets : Public vs. private health insurance schemes, asymmetric information and agency, moral hazard and adverse selection.

• Reforming health care : Goals of reform, cost containment, efficiency and equity, extending insurance coverage, costs of universal coverage.

Part III (7 hours) : Economics of the Environment

• Overview : Economics and Environment :

- A framework of analysis, environmental microeconomics and macroeconomics.
- The environment as a public good.
- The global commons

• Ecological Economics and the Economic analysis of Environmental Issues :

- Valuing the environment, accounting for environmental costs, internalizing environmental costs, optimal pollution, the Coase theorem.
- Environmentally-adjusted national income accounts, the Genuine progress indicator, the better life index, environmental assets accounts.

• Environmental Health Policy : Impacts and Policy Responses :

- Measuring the economic cost of environmental impacts on health.
- Economic analysis and assessments of the performance of alternative policies in areas such as climate change, outdoor air pollution, water and sanitation.

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Introduction to corporate finance - Financial econometrics (4 ECTS)

### Introduction to corporate finance

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Financial econometrics

## CONTENT

1. Analyzing the properties of financial time series : application to French stock markets

The data consists of the stocks of the French CAC40 on a daily basis since 1980. Data are provided in excel format and need to be download to GRETL. Different companies are used as examples.

- Computing returns and historical volatility and analyzing their graphs (mean, variance, skewness and kurtosis, quantiles, min and max, autocorrelation)
- Analyzing the distributions of returns : non-parametric approaches (histograms and CDF based on kernels ; normality tests : QQ plot, Shapiro-Wilkinson, Doornik-Hansen, Jarque-Bera, etc.)
- Informal presentation of stable distributions : index of stability, skewness parameter, scale parameter, location parameter
- Example of parametrization of a stable distribution : the regression analysis of power law distributions.

2. Regression analysis of financial data

2.1.Evaluating the performance of a money manager : CAPM model

The data consist of the S&P 500 and some of its components (General Electric, Ford, Microsoft, ORACLE) and the 3-month Treasury bill).

- Estimate of the Betas using OLS and GLS
- Test of the CAPM using a two-pass regression
- The Jensen measure to evaluate manager performance.

2.2. Modellling the term structure of interest rates

The data consist of the Government zero-coupon bond yield taken at a daily frequency from 1990 to 2017 with several maturities : 6 months, 1 year, 2 years, 4, years, 4 years, 5 years, 7 years and 10 years.

- Analyzing some basic stylized facts of government bond yields (graphs of term to maturity, statistical properties, normality tets, correlation matrix, etc…).
- Recall on asset pricing, Duffie-Kan affine models and the decomposition of the yield curve.
- Decomposition of the tield curve using the Diebold’s regression approach : Level, slope and curvature curves.
- Factor models : a basic presentation of Kalman filter methodology and applications to the yield curve.

3.Some benchmark models for forecasting and trading models

The data consists of US/euro, US/Japan, US/UK exchange rate (daily) from 1999 and 1977 to 2017.

3.1.Models of naïve and MACD (moving average) strategies

3.2.ARMA models (identification via ACF and PACF, estimation, residual tests and forecasts)

3.3.Dectecting long-range dependence structure : an introduction to ARFIMA models

3.4.Introduction to stochastic volatility models : Harvey models and ARCH-GARCH models (tests and estimation).

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Software for economists III - International trade (4 ECTS)

### Software for economists III

## CONTENT

This teaching unit aims at providing the fundamental basis of the use of R software (or the RStudio IDE) and R programming. The courses will be illustrated with exercises using the statistical environment R (http://www.r-project.org/) which is free, open-source free and multiplatform, or via the RStudio IDE. The organization of the course will make progressive the acquisition of the knowledge and the mastery of the R statistical tool. It aims to make the student more autonomous when faced to classical problem of statistical modelling or data analysis, which can be found in the fields of economics.

**Course outline :**

- Introduction (history).
- Basic handling (data management in R).
- Creating R functions.
- Loops, tests, vectorization.
- R Graphics.
- Application to modelling (regression/classification).

## VOLUME OF TEACHINGS

- Tutorials:
**18**hours

### International trade

## CONTENT

The aim of this course is to provide students the analytical tools that are essential to understand the causes and consequences of international trade. We will focus on some key questions as why nations trade, what they trade and who gains (or not) from trade. We will then analyse the reasons for countries to limit or regulate the exchange of goods and study the effects of such policies on development and inequality. We will also tackle some aspects of the globalization process like international norms, labor standards, firms’ organization, etc. We will heavily rely on formal economic modelling to help us understand issues of international trade.

**Course outline :**

1. Introduction – Basic facts

2. The Ricardian model

3. The Specific Factors model

4. The Hecksher-Ohlin Model

5. Trade theory with firm-level heterogeneity

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### M2 FQA (AN) (60 ECTS)

### S3 M2 FQA (SE) (30 ECTS)

### Theory of financial markets (6 ECTS)

### Models of finance

## CONTENT

The aim of this course is to give some general concepts that found the main models of finance. This in order to first better understand the jungle of financial products and second to understand the functioning of markets.

**Course outline :**

Chapter 1 – Introduction

1. First questions

2. Assets

3. Functioning of trading

4. Two first models : risk neutral valuation

Chapter 2 – Static model : arbitrage free condition

1. No arbitrage condition in a static model

2. Mathematical appendix

Chapter 3 – Dynamics (finite discrete models)

1. The tree of states of nature

2. Stochastic process on a tree

3. No arbitrage condition on a dynamic model

4. Risk neutral probability

5. The Cox Ross Rubinstein model

6. Reformulation : filtration and tree

7. Appendix : the example of a random walk

Chapter 4 – Continuous models

1. The “continuous random walk” : Brownian motion

2. Arbitrage free equation

3. The Black and Scholes model

4. Appendix : conditional expectation

Chapter 5 – Microstructure and behaviour models

1. The market efficiency hypothesis

2. The Competitive Rational Expectation Equilibrium

3. Bid ask spread (Glosten and Molgrom)

4. High frequency trading : arm’s race

5. The capital asset pricing model

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Portfolio management

## CONTENT

The objective of this series of lectures is to acquaint with the theory of finance and to see how it applies in practice. We revisit the fundamental asset pricing models, in particular the CAPM, which we will estimate in class on market data. The students will construct portfolios, using traditional techniques such as Markowitz’ mean-variance optimization and modern smart techniques. The students will build and manage fictive investment portfolios containing equities, bonds and currencies. Case studies will be done in class that I have come across in my work as a quant research analyst with asset management firms.

**Course outline :**

1. Introduction to portfolio management (3h)

On the basis of an investment example designed by Elton et al., concepts such as portfolio risk, risk decomposition, the efficient frontier, the Sharpe ratio will be revisited The students will do elementary exercises (e.g. estimate market betas), estimate a one-factor risk model and carry out a mean-variance optimization in Excel.

2. Equity investing (3h)

We look at risk measures, in particular volatility and dispersion in the CAC40- and DAX30. We review factor investing techniques.

3. Investment strategies (6h)

Most of this material cannot be found in finance textbooks. We construct portfolios that correspond to the investment objectives such as market replication, outperformance, capital protection, yield harvesting and impact investing. The construction process is materially different for each of these objectives.

4. Bond investing (6h)

The characteristics of fixed-income securities are discussed, for corporate bonds and state obligations separately, and the way to take them into consideration in a bond investment process.

5. Currency investing (3h)

On the basis of a ten-currency investment example, the students will familiarize with concepts such as carry trading, the interest rate parity, purchasing power parity, the Siegel paradox and currency hedging.

6. Real assets (3h)

We look at non-listed assets such as real estate, private equity, private debt and infrastructure investment vehicles. An innovative means to measure risk is presented.

7. Miscellaneous : asset allocation & bond scoring (3h)

We look at the asset allocation problem Central Banks typically face when allocating their foreign reserves. We look at bond scoring models that give estimates of the default probability and of the market liquidity of bond issues.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Economic and financial analyses (6 ECTS)

### Corporate finance I

## CONTENT

Does the choice of capital structure affect the value of the firm ?

The goal of the course is to investigate how the corporate finance field has addressed this question.

**Course outline :**

- Introduction to the 4 steps of financial analysis
- Capital Structure in a Perfect Market
- Debt and Taxes
- Financial Distress, Managerial Incentives, and Information
- Payout Policy

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Economics of risk and insurance

## CONTENT

The aim of this course is – in a first part – to present decision and contract theories in a risky context. In the second part, we apply it to insurance demand and show how individual behaviours aggregate in the insurance market and how prices form.

**Course outline :**

Chapter 1 - Risk and measures of risk (Dominique Henriet, 9h)

1. Assumptions on risk

2. Risk Analysis

2.1 Cumulative Distribution function

2.2 Stochastic dominance of degree 1

2.3 Quantile Function and Value at Risk

3. Spread Analysis

3.1 Expected Shortfall, Lorenz function

3.2 Mean Preserving Concentration

3.3 Measures based on the quantile function.

3.4 Coherent risk measures

4. Second degree Stochastic dominance

4.1 Mean preserving spread

5. Expected utility hypothesis

6. Dual criterion

7. Ambiguity

Chapter 2 – Insurance economics (Renaud Bourlès, 12h)

1. The single risk model

1.1 Mossin’s model

1.2 Wealth effect

1.3 Price effect

2. Product differentiation

2.1 Introducing heterogeneity in Mossin’s model

2.2 Measuring the probability of damage : scoring methods

2.3 Estimating scoring models

3. Unobservable criteria

3.1 The adverse selection problem

3.2 Self-selection : the Rothschild-Stiglitz model

3.3 Equilibrium existence

4. Moral hazard

4.1 Self-insurance and its consequences

4.2 Self-protection and moral hazard

4.3 Ex-post moral hazard : the case of insurance fraud

5. Extensions and exercises

5.1 Extensions of Mossin’s model

5.2 Insurance demand and exogenous risk

5.3 On the value of genetic information

5.4 Genetic information and self-insurance

5.5 Health risks and bidimensional utility

5.6 Life insurance and savings

Chapter 3 – Market & Counterparty Risk Management

1. Risk Management in Banks

2. Markets Risks

2.1 Sensitivities

2.2 Value at Risk (VaR)

2.3 Limitations of the VaR

2.4 Case Study

3. Counterparty Risks

3.1 Definition and key elements

3.2 Potential Future Expose (PFE) and Expected Positive Exposure (EPE)

3.3 Credit Valuation Adjustment (CVA)

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Mathematics and statistics for finance (6 ECTS)

### Stochastic finance

## CONTENT

The aim of the course is to provide students with mathematical methods that allow valuating financial assets.

**Course outline :**

1. Gaussian variables and stochastic processes

1.1 Unidimensional Gaussian variable

1.2 Gaussian vectors

1.3 Stochastic processes

2. Brownian motion

2.1 Construction as a Gaussian process

2.2 Expansion, Markov property and martingale

2.3 Invariance property

2.4 Trajectorial property

2.5 Complement on Brownian bridge

3. Stochastic integration and semimartingale

3.1 Integrating with respect to a Brownian motion

3.2 Introduction to the general theory of stochastic integration

3.3 Itô formula and first applications

4. Stochastic differential equation

4.1 Elements of motivation

4.2 Strong solutions

4.3 Some examples

5. Parabolic SDE, brownian diffusion and semigroups

5.1 Brownian motion and linear parabolic SDE

5.2 The general Feynman-Kac formula

5.3 Semigroups

6. Change of measure

6.1 Wiener space

6.2 Change of measure and Girsanov theorm

7. Introduction to financial mathematics

7.1 Black and Scholes model

7.2 Portfolio and option replication

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics of banking and finance

## CONTENT

This course presents the econometric methods used to measure and forecast financial risks. Different models will be studied. These models make it possible to model the dynamics of prices (or returns), ie. the conditional mean, the conditional variance, but also the higher moments (asymmetry, thickness of the distribution tails). Part of this course will also deal with the dependence between the returns of several assets.

**Course outline :**

- Conditional mean
- Conditional variance
- Estimation
- Specification tests
- Forecast
- Value-at-risk
- Multivariate models

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Quantitative methods in finance and insurance (6 ECTS)

### Big data and finance

## CONTENT

The course presents the last developments around the use of big data technics in finance. The first part offers an overview of the various recent applications to corporate finance and financial regulation. The second concentrates on the use of big data and associated models in market finance. The third and last part highlights the role of these methods in insurance and reinsurance market.

**Course outline :**

Part 1 Overview of the applications of Big data in finance (6h, Pierre Bittner)

1– The interest of big data in finance

1.1 – Reminder on Big data

1.2 – Big data and decision

1.3 – Big data and market supervision

2– Case study in finance

2.1 – Applications to corporate and investment banking

2.2 – Regulatory challenges

Part 2 : Big data and market finance (12h, Yoann Bourgeois)

1- Realized Volatility

1.1- Continuous time pricing fundamentals

1.1.1 Brownian motion and random walk

1.1.2 Stochastic Differential Equation/ Stochastic Integrals

1.1.3 Quadratic Variation

1.1.4 Implied volatility in Black Scholes

1.2- Realized Volatility

1.2.1 Unbiased estimators

1.2.3 Confidence intervals

1.2.3 Application FX market

1.3-RV and integrated variance

1.3.1 Seasonality

1.3.2 The impact of periodic events on the RV.

1.3.3 Application FX market

2- Bonds portfolio automatic engine

2.1 Definitions (Yields, Bond, Duration, P&L of a bond etc.)

2.2 Bonds clustering (PCA+KMeans)

2.3 The reference curve construction

2.3.1 Regression

2.3.2 Cubic Splines

2.4 Z-Score and momentum to sort bonds

2.5 Reference bonds replication

2.6 Application France 10Y reference bond.

3- Intraday hedging of FX options

3.1 SABR model

3.2 Gatheral parametric local volatility model

3.3 Intraday model calibrations

3.4 Tichonov Regularization

3.5 The use of risk neutral distribution quantiles and moments

3.6 Application FX vanilla options

Part 3 : Big data and insurance (6h, Serdar Coskun)

This part presents, via recent cases, the utility of big data and insurance and reinsurance markets. It also presents the most recent progress in the « insurtech » market.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Actuarial science I

## CONTENT

The aim of the course is to present the main issues related to the pricing of insurance products as well as the fundamental differences between life and non-life insurance.

**Course outline :**

Chapter 1 – Introduction to actuarial science (R. Bourlès, 6h)

1. Life insurance model

1.1 Mortality risk and pricing errors

1.2 Main insurance products : fair premiums and prudent pricing

1.3 Actuarial Present Value and Notations

1.4 Exercises

2. Non-life specificities

2.1 Provisioning

2.2 The variability of non-life risks

2.3 The role of financial markets

Chapter 2 – Life Insurance, saving products, and accounting (X. Guerrault, 9h)

1. Introduction on Mathematical Reserves

2. Saving contracts and performance distribution mechanisms

3. Performance indicators for an insurance company

Chapter 3 – Non-Life Insurance (F. Derbez and R. Mouyrin, 9h)

1. Introduction (definition and example of claims)

2. Mechanisms of Non-Life Insurance

2.1. Generalities

2.2 Technical indicators

3. Pricing (modeling and examples)

4. Loss experience and reserving

4.1 Definitions

4.2 Deterministic methods

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Economics of finance (6 ECTS)

### Economics, finance and crises

## CONTENT

Using both empirical evidences and theoretical concepts, this course aims at explaining how economic and financial issues are closely related, and how shocks and crises can propagate. It also explains the interactions between financial markets and economic cycles (in light of the recent crises).

**Course outline :**

- Empirical Evidence on Financial Crises
- Financial frictions
- The financial crisis of 2006-2009
- Unconventional monetary policy
- European Sovereign Debt Crisis Discussion

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Innovation and finance

## CONTENT

This course presents recent financial innovations and their impact on financial markets.

**Course outline :**

Chapter 1 – Blockchain and applications (Jérôme Gonzalez, 12h)

1. Introduction (history, properties and use case)

2. Applications in finance and insurance

3. Focus on ICOs

4. Perspectives

Chapter 2 – Green finance and sustainable finance (Grégoire Hug, 6h)

1. Sustainable Finance

1.1. Socially Responsible Investment (SRI) history

1.2. ESG (Environmental Social & Governance) data

1.3. Investment strategies

1.4. Financial innovation

2. Green finance

2.1 COP21 implications on Finance

2.2 Carbon Footprint measurement applied to finance : Principle & bias

2.3 Case study

Chapter 3 – Crowdfinance and its impact on banking (François Fromaget, 6h)

1. Introduction : crowdlending and crowdfunding

2. How to measure and present default risk ?

3. Fintech and crowdfinance

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### S4 M2 FQA (SE) (30 ECTS)

### End-of-study internship with report and defence (24 ECTS)

### Elective courses, choose 2 among 4 (6 ECTS)

### Numerical methods for finance (3 ECTS)

### Numerical methods for finance

## VOLUME OF TEACHINGS

- Tutorials:
**5**hours

### Actuarial science II (3 ECTS)

### Actuarial science II

## CONTENT

The aim of this course is to present the recent developments in actuarial sciences, notably those related to prudential regulation.

**Course outline :**

1. Valuing an insurance portfolio

2. Introduction to reinsurance

3. Asset-liability management in insurance

4. Accounting and financial communication of insurance companies

5. The current regulation : Solvency 2

6. Long term care

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Corporate finance (3 ECTS)

### Corporate finance II

## CONTENT

The aim is to present the main tools of structured finance, for both project and corporate financing.

**Course outline :**

Chapter 1 – Corporate financing (Johannes Lock, 6h)

1. Leasing

2. LBO

Chapter 2 – Introduction to project financing (Medhi El Alaoui, 6h)

Chapter 3 – Financing of sustainable energy infrastructures (Philippe Genre et Amaury Schoenauer, 12h)

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Credit risk (3 ECTS)

### Credit risk

## CONTENT

To explain the evolution of banking regulation on credit risk since the financial crisis (Basel II, Basel III & future regulations)

To understand the notion of credit risk (theoretical models, measurement, pricing, management, etc...)

**Course outline :**

1. Introduction : bonds and OTC transactions

2. Modelling defaults : structural models and ratings

3. Structured financing : plain-vanilla, asset financing, securitization etc.

4. Banking regulation on credit risk

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Track FQA magistère option (OPPT) (144 ECTS)

### M1 Economics (magistère option) (AN) (72 ECTS)

### S1 M1 Economics magistère option (SE) (36 ECTS)

### Microeconomics I and II (6 ECTS)

### Microeconomics I

## CONTENT

The objective of this course is to provide students with the foundations of economic theory. The course covers the consumption and production theory and is textbook based. The difficulty and coverage compare to those of the main departments of economics worldwide.

__Course outline :__

The course is textbook based. Topic list : Technology, Profit Maximization, Profit Function, Cost minimization, Cost Function, Duality, Utility Maximization, Choice, Demand.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Microeconomics II

## CONTENT

**Course outline :**

The course is textbook based. Topics list : Exchange, Time, Equilibrium Analysis, Welfare.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics I and II (6 ECTS)

### Macroeconomics I

## CONTENT

Learn the basic models with microeconomic foundations used in modern macroeconomics. Be able to do dynamic analysis. Understand the concept of dynamic efficiency and the role of public expenditures.

**Course outline :**

1. Introduction with reminders on the Solow model

2. The Ramsey model

2.1. The framework

2.2. Existence and features of the steady state

2.3. Dynamic analysis

2.4. Extension : public spending

3. The overlapping generations model

3.1. The model with capital

3.2. Intertemporal equilibrium, steady states and dynamics

3.3. Optimality

3.4. Extensions : public spending ; rational bubbles

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics II

## CONTENT

The aim of the course is to present advanced macroeconomic topics related to the analysis of aggregate consumption, aggregate investment and modern business cycle analysis with the Real Business Cycle model.

**Course outline :**

Chap. I : Consumption theory

1. Consumption over the life cycle : the life-cycle/permanent income models

2. Introducing uncertainty – The random walk hypothesis

3. Market imperfections : the role of liquidity constraints

4. Extensions : risk aversion, precautionary savings

Chap. 2 : Investment theory

1. The neoclassical model of capital demand

2. Investment with and without capital adjustment costs : Q-theory models

3. Role of shocks : real shocks, news shocks, noise shocks

Chap. 3 : Real Business Cycles

1. Measuring business cycles : trend-cycle decompositions and stylized facts

2. The canonical RBC model

3. Evaluation of the model

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics I and II (6 ECTS)

### Econometrics I: linear model

## CONTENT

**Provide students with :**

- the basics of panel data econometrics (fixed effects models, error components model)
- the identification of endogeneity problems in econometric models and their treatment (instrumental variables, GMM, tests)

**Course outline :**

1. Introduction to panel data and panel data models

2. The fixed effects model

- Specification of the model
- Estimation of the model : the Within / LSDV estimator.
- Testing the absence of unobserved heterogeneity.

3. The error components model

- Specification of the model
- Estimation of the model : the GLS / FGLS estimators.
- Testing the absence of unobserved heterogeneity.
- Testing the absence of correlation of the effects : the Hausman test

4. Endogeneity issues

- Causes of endogeneity in econometric models : measurement errors, dynamic models, unobserved heterogeneity, etc.
- The instrumental variables estimator
- The GMM estimator
- Looking for instruments (the time-series case, the cross-section case, the panel data case).
- Testing the validity of instruments
- Testing the exogeneity of regressors

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics II: non linear model

## CONTENT

Provide students with the basics of the econometrics of non linear models for binary, multinomial, ordered and count dependent variables as well as models for censored and truncated variables.

**Course outline :**

1. Introduction to non-linear models in econometrics and a brief reminder about the maximum likelihood principle.

2. Models for binary dependent variables.

- The linear probability model.
- The Logit model.
- The Probit model.

3. Models for multinomial and ordered dependent variables.

4. Models for count data.

5. Models for truncated and censored variables.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Labor economics - Risk and incentives (6 ECTS)

### Labor economics

## CONTENT

The objective of this course is to provide students with the necessary analytical tools to be able to study the consequences of different institutions, human capital formation, discrimination and wage bargaining on the labor market.

**Course outline :**

Introductory Chapter :

- Presentation
- Objectives
- Evaluation
- Labor market Institutions and course outline

Chapter 1 : « Labor Supply and Labor Demand » :

- Key definitions
- Labor Supply
- Labor Demand
- Equilibrium

Chapter 2. « Minimun wage »

- Facts
- Classical analysis
- The monopsony case
- Dual labor markets

Chapter 3 : « Mandatory contributions and social benefits »

- Facts
- Classical analysis
- Accounting for wage rigidities

Chapter 4. « Labor Unions » :

- Facts : unions, collective bargaining, union density
- The objective of labor unions
- Models of collective bargaining
- Model of strikes
- Empirical evidence and policy issues

Chapter 5. « Discrimination » :

- Facts : gender and ethnic wage and employment gaps
- Economic theories on discrimination
- Measuring wage discrimination
- Empirical results in the literature and policy issues

Chapter 6. « Education and human capital formation » :

- Facts
- The theory of human capital
- Education as a signaling device
- Identifying the causal relation between education and income
- Returns to education : private vs social returns

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Risk and incentives

## CONTENT

The main objective of this course is to provide the students with a theoretical synthetic framework so that they can face the difficulties of the study of economic decisions under uncertainty. Two main general topics will be dealt with : (1) the theory of decision under uncertainty, and (2) the moral hazard issues between several economic agents.

**Course outline :**

Chapter 1 : Risk, uncertainty and strategies

- Introduction of the main concepts (risk, uncertainty, probability, moral hazard, adverse selection)
- Probabilistic framework (space of states, random variables)
- Numerical decision criteria (preferences, representation by a numerical criteria)
- Game theory, Principal-Agent model

Chapter 2 : Expected Utility

- The virtues of the expected utility (Saint-Petersburg paradox)
- The axiomatics of the expected utility (objective and subjective expected utility)
- The limits of the expected utility (Allais paradox, Ellsberg paradox)
- Generalisations of the expected utility (rank-dependent expected utility, Choquet expected utility)

Chapter 3 : Risk Aversion and Risk Measures

- Qualitative approach (certainty equivalent, risk premium, risk attitude)
- Quantitative approach (local measures of risk aversion)
- Stochastic dominance (first and second order)

Chapter 4 : Introduction to moral hazard issues

- Risk sharing and sharecropping contracts
- Credit with risk aversion of the borrower

Chapter 5 : Other applications

- Risky saving
- Application of the expected utility to static portfolio choice

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Methodology I (6 ECTS)

### Software for economists I

## CONTENT

Provide students with the basics of the statistical and econometric treatment of data using SAS, from the statistical description of the sample, the detection of outliers to the implementation of estimation techniques for linear and non-linear models.

**Course outline :**

1. Introduction to SAS : importing and managing data – proc import, proc contents, proc format, proc sort, proc surveyselect and introduction to SAS macro functions.

2. Describing the data : descriptive statistics with SAS – proc means, proc univariate, proc freq, proc tabulate, proc gplot.

3. Estimating and testing linear models : proc reg, proc glm, proc model, proc panel.

4. Estimating and testing non linear models : proc logistic, proc probit, proc model, proc genmod, proc nlmixed.

## VOLUME OF TEACHINGS

- Tutorials:
**24**hours

### Mathematics for economists

## CONTENT

The course intends to deepen the understanding of optimization theory with a geometric approach, and to introduce in a second part the study of dynamical systems.

__Course outline__

**I. Optimization with mixed constraints** a. Tangent cone and KKT conditions b. Mixed constraints problem c. Constraints qualification conditions d. Convex problems e. Saddle point and duality

II. **Dynamical systems** a. Introduction b. Systems of linear equations

- Constant coefficient : resolution, exponantial of matrices
- Dynamic of the solutions : steady state, stability, planar systems
- nonhomogeneous systems c. Systems of nonlinear differential equations
- Existence and uniqueness theorem
- Linearized system, Hartman-Grobman theorem

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Big Data (6 ECTS)

### Big data, challenges and opportunities

## VOLUME OF TEACHINGS

- Lectures:
**6**hours

### Programming for Big Data, an introduction to Python and SQL

## CONTENT

This course is aimed at teaching the basics of computer programming, with emphasis on its use in Big Data. Students will first become familiar with database management (relational or not). They will then learn the basics of programming with the computer language Python.

**Course outline :**

Chapter 1 : Relational databases

1. Introduction

2. The relational model

3. Relational algebra

4. SQL Language

5. Entity-Association Schemes

Chapter 2 : Non-relational databases

1. Introduction

2. Parallel Computing

3. Schemas, and non-relational databases

4. MongoDB

Chapter 3 : Introduction to Python

1. Variables et calculs

2. Strings, lists, tuples, dictionnaries

3. If… else conditions

4. Loops

5. Functions

6. Introduction to Numpy

7. Data handling with Pandas

8. Visualization

9. Parallel programming

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Big data softwares

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### S2 M1 Economics magistère option (SE) (36 ECTS)

### Microeconomics III and IV (6 ECTS)

### Microeconomics III - Game theory

## CONTENT

Introducing the basic concepts of Game Theory.

**Course outline :**

1. Complete information games (normal form, examples, analysis)

2. Mixed extension (lotteries, expected gain, mixed-strategy equilibrium)

3. Games with continuous actions (externalities,imperfect competition)

4. Incomplete information games (extensive form, subgame perfection)

5. Additional examples.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Microeconomics IV - Public economics

## CONTENT

The objective of this course is to study the role of state in the economy. It is designed to provide students with a broad overview of issues investigated in public economics. We will review the rational foundations of public intervention and explore some of the tools used by government to act : taxes and transfers, the provision of public goods, or the design of welfare schemes. Most topics will be approached from both theoretical and empirical points of view.

__Course outline :__

**Lecture 1 – Introduction to public economics**

- Foundations of public intervention – Normative and positive public economics – Some numbers about public intervention – Empirical methods for public economics

**Lecture 2 – Social choice and social welfare**

- Axiomatic approach to social choice – Social welfare functions

**Lecture 3 – Public goods and externalities**

- Public goods – Externalities

**Lecture 4 – Taxation of commodities**

- Tax incidence – Optimal commodity taxation

**Lecture 5 – Taxation of labor**

- Optimal labor taxation – Some empirics around labor taxation

**Lecture 6 – Taxation of capital**

- Taxes in an intertemporal framework – Optimal capital income taxation – Taxation of inheritances

**Lecture 7 – Social insurance**

- Unemployment insurance and workers’ compensation – Disability insurance – Health insurance

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Big Data (6 ECTS)

### Advanced SAS

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Introduction to machine learning

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics III and IV (6 ECTS)

### Macroeconomics III

## CONTENT

This course follows Macroeconomics II and it goes deeper in the description of micro-founded models by introducing market frictions into the RBC model. The DSGE-New Keynesian model which includes nominal rigidity is a natural extension of the RBC model to analyze monetary policy / fiscal policy. Although this course is mainly theoretical, lectures will be motivated by stylized facts and the empirical performance of business cycle models will be discussed.

**Course outline :**

Chapter 1 : Nominal rigidities (1) Introducing money in RBC model (2) Monopolistic competition (3) Price rigidity (4) Exercises

Chapter 2 : Monetary and Fiscal policy (1) Monetary policy analysis (2) Fiscal policy analysis (3) New topics in macroeconomics (ZLB, forward guidance…)

(4) Exercises

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Macroeconomics IV

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Méthodologie (6 ECTS)

### Software for economists II

## CONTENT

The objective of this course is twofold. Firstly, to study how to use and manipulate databases with Stata and secondly, to perform empirical analysis in relation with the concepts learned in the time series and econometric methods of evaluation classes. After a short introduction to Stata, the course will be divided into tasks-oriented sessions (with mini-projects and exercises) during which the students will perform empirical analysis using databases such as the World Values Survey, the French Labor Force Survey, the National Supported Work data, etc.

**Course outline :**

Lecture 1 : Introduction to Stata and database manipulation

Why using Stata – What Stata looks like – Importing and reading data into Stata – Examining the data – Saving the dataset – Keeping track of things – Organizing datasets – Creating new variables – Panel data manipulation

Lecture 2 : Graphs and linear regressions

Histograms – Two-dimensional graphs – Linear regressions – Post-estimation – Extracting results – Hypothesis testing – Interaction terms – Non-linearity – Fixed effects

Lecture 3 : Endogeneity and public policies econometrics

Randomized control trials – Difference-in-differences – Validity checks

Lecture 4 : Time series

Stationary and non-stationary processes

## VOLUME OF TEACHINGS

- Tutorials:
**24**hours

### Mathematics for finance

## CONTENT

**Objectives :**

Introducing elementary tools to analyse discrete and continuous-time random processes.

**Roadmap :**

1. Markov chains

1.1. Introductory Example : random walks

1.2. Markov chains on a finite state space

1.3. Markov chains on countable state spaces

1.3.1. States classification

1.3.2. Asymptotic results

2. Markovian processes in continuous time

2.1. Poisson processes

2.2. Continuous-time Markov processes

2.3. Queueing theory

3. Discrete-time random processes

3.1. Conditional expectation

3.2. Martingales

3.3. Stopping time

3.4. Convergence theorems

3.5. Applications

4. Introduction to continuous-time stochastic processes : Brownian motion

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Vocational courses (6 ECTS)

### Quantitative marketing

## VOLUME OF TEACHINGS

- Lectures:
**12**hours

### Software: R

## VOLUME OF TEACHINGS

- Lectures:
**12**hours

### Economic policy II

## VOLUME OF TEACHINGS

- Lectures:
**12**hours

### Insurance mechanisms

## VOLUME OF TEACHINGS

- Lectures:
**12**hours

### Oral training on Economics topics

## VOLUME OF TEACHINGS

- Tutorials:
**6**hours

### Oral training in English

## VOLUME OF TEACHINGS

- Tutorials:
**6**hours

### Elective courses, choose 2 among 6 (6 ECTS)

### Introduction to corporate finance (3 ECTS)

### Introduction to corporate finance

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Project management (3 ECTS)

### Project management

## CONTENT

Designing and managing development aid projects according to international standards.

**Course outline :**

The students will learn and practice how to build a development program.

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Health and environmental economics (3 ECTS)

### Health and environmental economics

## CONTENT

The goal of this course is to bring together health and environmental economics as two narrow fields within the discipline of economics. This shall be done by identifying the interactions and intersections between health and environmental issues, describing the main economic properties that health and environment do have in common (market failure, externalities, government involvements …). This shall be followed by delineating the unique features of health and environment that make of them two distinct topics of study. Following this line of reasoning, the course shall, then, present two self-contained parts devoted to health economics and environmental economics. Each part shall present the workhorse analytical concepts and methods used by economists to explore specific issues relating to the two subfields. The course shall emphasize the use of economic evidence to identify priority issues and the most effective policies for health and environment. Examples and experiences of the kinds of topics that are addressed shall be provided all through the course.

**Course outline :**

Part I (4 hours) Overview : The links between health, environment and the economy

• Economic properties of health and environment

- What distinguishes “health goods” from “environmental goods” ?
- Typology of goods : Pure vs. impure public goods, private vs. publicly-provided private good, global vs. local public goods.

• The economic valuation approach :

- The theory of externalities
- Welfarism vs. extra-welfarism analysis
- Cost-benefit analysis, cost-effectiveness analysis, cost-utility analysis.
- Revealed vs. stated-preferences methods

• Government intervention and regulations

- Why do governments provide goods that are not pure public goods ? The case of health care services.
- What are the special characteristics and challenges of the “global public goods” ? The case of global climate change
- Rationing devices for publicly-provided goods (User charges, uniform provision, queuing).
- Efficiency conditions for public and pure public goods : Collective demand curve and provision of public goods.

Part II (7 hours) : Economics of Health and Health Care

• Overview : Health economics as a field of inquiry

• Health care market structure, conduct and performance :

- Do the law of supply and demand apply to health and health care ?
- What makes health and health care different ?
- Demand for health and health care : Health behavior
- Supply of health care : Production, provision and costs of health care.
- Health insurance markets : Public vs. private health insurance schemes, asymmetric information and agency, moral hazard and adverse selection.

• Reforming health care : Goals of reform, cost containment, efficiency and equity, extending insurance coverage, costs of universal coverage.

Part III (7 hours) : Economics of the Environment

• Overview : Economics and Environment :

- A framework of analysis, environmental microeconomics and macroeconomics.
- The environment as a public good.
- The global commons

• Ecological Economics and the Economic analysis of Environmental Issues :

- Valuing the environment, accounting for environmental costs, internalizing environmental costs, optimal pollution, the Coase theorem.
- Environmentally-adjusted national income accounts, the Genuine progress indicator, the better life index, environmental assets accounts.

• Environmental Health Policy : Impacts and Policy Responses :

- Measuring the economic cost of environmental impacts on health.
- Economic analysis and assessments of the performance of alternative policies in areas such as climate change, outdoor air pollution, water and sanitation.

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### Evaluation by econometric methods (3 ECTS)

### Evaluation by econometric methods

## CONTENT

The objective of the course is to offer M1 students with an overview of the main empirical methods used for the evaluation of public policies. We will study key articles taken from various applied economics literature (health, education or activive labor policies). Practical case studies on STATA will be offered all along. We will point out advantages and limits of each method as well as guide in the selection of the appropriate method.

**Course outline :**

Introduction

1. Why evaluate ? What do we evaluate ? What is the objective ?

2. Potential outcome framework

3. Treatment effects and counterfactuals

4. Selection bias

Chapter 1 : Randomized experiments

1. Random assignment

2. Underlying assumptions

3. Study of 2 empirical papers using the method

4. Randomized experiments in practice

Running example : exercise on National Supported Work (NSW) data

Chapter 2 : Natural experiment : Difference-in-difference method

1. Model and underlying assumptions

2. Study of 2 empirical papers using the method

3. Extensions

4. D-in-D in practice

Running example : exercise on National Supported Work (NSW) data

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### International trade (3 ECTS)

### International trade

## CONTENT

The aim of this course is to provide students the analytical tools that are essential to understand the causes and consequences of international trade. We will focus on some key questions as why nations trade, what they trade and who gains (or not) from trade. We will then analyse the reasons for countries to limit or regulate the exchange of goods and study the effects of such policies on development and inequality. We will also tackle some aspects of the globalization process like international norms, labor standards, firms’ organization, etc. We will heavily rely on formal economic modelling to help us understand issues of international trade.

**Course outline :**

1. Introduction – Basic facts

2. The Ricardian model

3. The Specific Factors model

4. The Hecksher-Ohlin Model

5. Trade theory with firm-level heterogeneity

## VOLUME OF TEACHINGS

- Lectures:
**18**hours

### M2 track FQA : magistère option (AN) (72 ECTS)

### S3 M2 FQA magistère option (SE) (36 ECTS)

### Theory of financial markets (6 ECTS)

### Models of finance

## CONTENT

The aim of this course is to give some general concepts that found the main models of finance. This in order to first better understand the jungle of financial products and second to understand the functioning of markets.

**Course outline :**

Chapter 1 – Introduction

1. First questions

2. Assets

3. Functioning of trading

4. Two first models : risk neutral valuation

Chapter 2 – Static model : arbitrage free condition

1. No arbitrage condition in a static model

2. Mathematical appendix

Chapter 3 – Dynamics (finite discrete models)

1. The tree of states of nature

2. Stochastic process on a tree

3. No arbitrage condition on a dynamic model

4. Risk neutral probability

5. The Cox Ross Rubinstein model

6. Reformulation : filtration and tree

7. Appendix : the example of a random walk

Chapter 4 – Continuous models

1. The “continuous random walk” : Brownian motion

2. Arbitrage free equation

3. The Black and Scholes model

4. Appendix : conditional expectation

Chapter 5 – Microstructure and behaviour models

1. The market efficiency hypothesis

2. The Competitive Rational Expectation Equilibrium

3. Bid ask spread (Glosten and Molgrom)

4. High frequency trading : arm’s race

5. The capital asset pricing model

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Portfolio management

## CONTENT

The objective of this series of lectures is to acquaint with the theory of finance and to see how it applies in practice. We revisit the fundamental asset pricing models, in particular the CAPM, which we will estimate in class on market data. The students will construct portfolios, using traditional techniques such as Markowitz’ mean-variance optimization and modern smart techniques. The students will build and manage fictive investment portfolios containing equities, bonds and currencies. Case studies will be done in class that I have come across in my work as a quant research analyst with asset management firms.

**Course outline :**

1. Introduction to portfolio management (3h)

On the basis of an investment example designed by Elton et al., concepts such as portfolio risk, risk decomposition, the efficient frontier, the Sharpe ratio will be revisited The students will do elementary exercises (e.g. estimate market betas), estimate a one-factor risk model and carry out a mean-variance optimization in Excel.

2. Equity investing (3h)

We look at risk measures, in particular volatility and dispersion in the CAC40- and DAX30. We review factor investing techniques.

3. Investment strategies (6h)

Most of this material cannot be found in finance textbooks. We construct portfolios that correspond to the investment objectives such as market replication, outperformance, capital protection, yield harvesting and impact investing. The construction process is materially different for each of these objectives.

4. Bond investing (6h)

The characteristics of fixed-income securities are discussed, for corporate bonds and state obligations separately, and the way to take them into consideration in a bond investment process.

5. Currency investing (3h)

On the basis of a ten-currency investment example, the students will familiarize with concepts such as carry trading, the interest rate parity, purchasing power parity, the Siegel paradox and currency hedging.

6. Real assets (3h)

We look at non-listed assets such as real estate, private equity, private debt and infrastructure investment vehicles. An innovative means to measure risk is presented.

7. Miscellaneous : asset allocation & bond scoring (3h)

We look at the asset allocation problem Central Banks typically face when allocating their foreign reserves. We look at bond scoring models that give estimates of the default probability and of the market liquidity of bond issues.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Economic and financial analyses (6 ECTS)

### Corporate finance I

## CONTENT

Does the choice of capital structure affect the value of the firm ?

The goal of the course is to investigate how the corporate finance field has addressed this question.

**Course outline :**

- Introduction to the 4 steps of financial analysis
- Capital Structure in a Perfect Market
- Debt and Taxes
- Financial Distress, Managerial Incentives, and Information
- Payout Policy

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Economics of risk and insurance

## CONTENT

The aim of this course is – in a first part – to present decision and contract theories in a risky context. In the second part, we apply it to insurance demand and show how individual behaviours aggregate in the insurance market and how prices form.

**Course outline :**

Chapter 1 - Risk and measures of risk (Dominique Henriet, 9h)

1. Assumptions on risk

2. Risk Analysis

2.1 Cumulative Distribution function

2.2 Stochastic dominance of degree 1

2.3 Quantile Function and Value at Risk

3. Spread Analysis

3.1 Expected Shortfall, Lorenz function

3.2 Mean Preserving Concentration

3.3 Measures based on the quantile function.

3.4 Coherent risk measures

4. Second degree Stochastic dominance

4.1 Mean preserving spread

5. Expected utility hypothesis

6. Dual criterion

7. Ambiguity

Chapter 2 – Insurance economics (Renaud Bourlès, 12h)

1. The single risk model

1.1 Mossin’s model

1.2 Wealth effect

1.3 Price effect

2. Product differentiation

2.1 Introducing heterogeneity in Mossin’s model

2.2 Measuring the probability of damage : scoring methods

2.3 Estimating scoring models

3. Unobservable criteria

3.1 The adverse selection problem

3.2 Self-selection : the Rothschild-Stiglitz model

3.3 Equilibrium existence

4. Moral hazard

4.1 Self-insurance and its consequences

4.2 Self-protection and moral hazard

4.3 Ex-post moral hazard : the case of insurance fraud

5. Extensions and exercises

5.1 Extensions of Mossin’s model

5.2 Insurance demand and exogenous risk

5.3 On the value of genetic information

5.4 Genetic information and self-insurance

5.5 Health risks and bidimensional utility

5.6 Life insurance and savings

Chapter 3 – Market & Counterparty Risk Management

1. Risk Management in Banks

2. Markets Risks

2.1 Sensitivities

2.2 Value at Risk (VaR)

2.3 Limitations of the VaR

2.4 Case Study

3. Counterparty Risks

3.1 Definition and key elements

3.2 Potential Future Expose (PFE) and Expected Positive Exposure (EPE)

3.3 Credit Valuation Adjustment (CVA)

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Mathematics and statistics for finance (6 ECTS)

### Stochastic finance

## CONTENT

The aim of the course is to provide students with mathematical methods that allow valuating financial assets.

**Course outline :**

1. Gaussian variables and stochastic processes

1.1 Unidimensional Gaussian variable

1.2 Gaussian vectors

1.3 Stochastic processes

2. Brownian motion

2.1 Construction as a Gaussian process

2.2 Expansion, Markov property and martingale

2.3 Invariance property

2.4 Trajectorial property

2.5 Complement on Brownian bridge

3. Stochastic integration and semimartingale

3.1 Integrating with respect to a Brownian motion

3.2 Introduction to the general theory of stochastic integration

3.3 Itô formula and first applications

4. Stochastic differential equation

4.1 Elements of motivation

4.2 Strong solutions

4.3 Some examples

5. Parabolic SDE, brownian diffusion and semigroups

5.1 Brownian motion and linear parabolic SDE

5.2 The general Feynman-Kac formula

5.3 Semigroups

6. Change of measure

6.1 Wiener space

6.2 Change of measure and Girsanov theorm

7. Introduction to financial mathematics

7.1 Black and Scholes model

7.2 Portfolio and option replication

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Econometrics of banking and finance

## CONTENT

This course presents the econometric methods used to measure and forecast financial risks. Different models will be studied. These models make it possible to model the dynamics of prices (or returns), ie. the conditional mean, the conditional variance, but also the higher moments (asymmetry, thickness of the distribution tails). Part of this course will also deal with the dependence between the returns of several assets.

**Course outline :**

- Conditional mean
- Conditional variance
- Estimation
- Specification tests
- Forecast
- Value-at-risk
- Multivariate models

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Quantitative methods in finance and insurance (6 ECTS)

### Big data and finance

## CONTENT

The course presents the last developments around the use of big data technics in finance. The first part offers an overview of the various recent applications to corporate finance and financial regulation. The second concentrates on the use of big data and associated models in market finance. The third and last part highlights the role of these methods in insurance and reinsurance market.

**Course outline :**

Part 1 Overview of the applications of Big data in finance (6h, Pierre Bittner)

1– The interest of big data in finance

1.1 – Reminder on Big data

1.2 – Big data and decision

1.3 – Big data and market supervision

2– Case study in finance

2.1 – Applications to corporate and investment banking

2.2 – Regulatory challenges

Part 2 : Big data and market finance (12h, Yoann Bourgeois)

1- Realized Volatility

1.1- Continuous time pricing fundamentals

1.1.1 Brownian motion and random walk

1.1.2 Stochastic Differential Equation/ Stochastic Integrals

1.1.3 Quadratic Variation

1.1.4 Implied volatility in Black Scholes

1.2- Realized Volatility

1.2.1 Unbiased estimators

1.2.3 Confidence intervals

1.2.3 Application FX market

1.3-RV and integrated variance

1.3.1 Seasonality

1.3.2 The impact of periodic events on the RV.

1.3.3 Application FX market

2- Bonds portfolio automatic engine

2.1 Definitions (Yields, Bond, Duration, P&L of a bond etc.)

2.2 Bonds clustering (PCA+KMeans)

2.3 The reference curve construction

2.3.1 Regression

2.3.2 Cubic Splines

2.4 Z-Score and momentum to sort bonds

2.5 Reference bonds replication

2.6 Application France 10Y reference bond.

3- Intraday hedging of FX options

3.1 SABR model

3.2 Gatheral parametric local volatility model

3.3 Intraday model calibrations

3.4 Tichonov Regularization

3.5 The use of risk neutral distribution quantiles and moments

3.6 Application FX vanilla options

Part 3 : Big data and insurance (6h, Serdar Coskun)

This part presents, via recent cases, the utility of big data and insurance and reinsurance markets. It also presents the most recent progress in the « insurtech » market.

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Actuarial science I

## CONTENT

The aim of the course is to present the main issues related to the pricing of insurance products as well as the fundamental differences between life and non-life insurance.

**Course outline :**

Chapter 1 – Introduction to actuarial science (R. Bourlès, 6h)

1. Life insurance model

1.1 Mortality risk and pricing errors

1.2 Main insurance products : fair premiums and prudent pricing

1.3 Actuarial Present Value and Notations

1.4 Exercises

2. Non-life specificities

2.1 Provisioning

2.2 The variability of non-life risks

2.3 The role of financial markets

Chapter 2 – Life Insurance, saving products, and accounting (X. Guerrault, 9h)

1. Introduction on Mathematical Reserves

2. Saving contracts and performance distribution mechanisms

3. Performance indicators for an insurance company

Chapter 3 – Non-Life Insurance (F. Derbez and R. Mouyrin, 9h)

1. Introduction (definition and example of claims)

2. Mechanisms of Non-Life Insurance

2.1. Generalities

2.2 Technical indicators

3. Pricing (modeling and examples)

4. Loss experience and reserving

4.1 Definitions

4.2 Deterministic methods

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### End-of-study project (6 ECTS)

### Big Data (6 ECTS)

### IT tools for Big Data, a deeper view

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Advanced machine learning

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### S4 M2 FQA magistère option (SE) (36 ECTS)

### End-of-study internship with report and defence (24 ECTS)

### Big data IV (6 ECTS)

### Managing Big Data with SAS

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Hands-on project

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Elective courses, choose 2 among 4 (6 ECTS)

### Numerical methods for finance (3 ECTS)

### Numerical methods for finance

## VOLUME OF TEACHINGS

- Tutorials:
**5**hours

### Actuarial science II (3 ECTS)

### Actuarial science II

## CONTENT

The aim of this course is to present the recent developments in actuarial sciences, notably those related to prudential regulation.

**Course outline :**

1. Valuing an insurance portfolio

2. Introduction to reinsurance

3. Asset-liability management in insurance

4. Accounting and financial communication of insurance companies

5. The current regulation : Solvency 2

6. Long term care

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Corporate finance (3 ECTS)

### Corporate finance II

## CONTENT

The aim is to present the main tools of structured finance, for both project and corporate financing.

**Course outline :**

Chapter 1 – Corporate financing (Johannes Lock, 6h)

1. Leasing

2. LBO

Chapter 2 – Introduction to project financing (Medhi El Alaoui, 6h)

Chapter 3 – Financing of sustainable energy infrastructures (Philippe Genre et Amaury Schoenauer, 12h)

## VOLUME OF TEACHINGS

- Lectures:
**24**hours

### Credit risk (3 ECTS)

### Credit risk

## CONTENT

To explain the evolution of banking regulation on credit risk since the financial crisis (Basel II, Basel III & future regulations)

To understand the notion of credit risk (theoretical models, measurement, pricing, management, etc...)

**Course outline :**

1. Introduction : bonds and OTC transactions

2. Modelling defaults : structural models and ratings

3. Structured financing : plain-vanilla, asset financing, securitization etc.

4. Banking regulation on credit risk

## VOLUME OF TEACHINGS

- Lectures:
**24**hours