**Summer School on Mathematical Methods in Finance and Economy**

31/May – 04/June/2010

Hanoi Center for Financial and Industrial Mathematics

Hanoi National University of Education

**Targeted audience**

Graduate students and researchers in finance, economics, and mathematics

People working in the financial industry (investment, insurance, …)

**Programme**

This School will consist of 4 main intensive minicourses (about 6 hours per course), computer sessions, and some research talks.

The four minicourses are:

*Time Series Applied to Finance*, by Anne Van Hems (Professor at Toulouse Business School)

*Non-Parametric Models With Applications To Production Frontiers*, by Michel Simoni (Research Director at INRA)

*Scoring*, by Christine Thomas-Agnan (Professor at Toulouse School of Economics)

*Quantitative Portfolio Management*, by Nguyen Tien Zung (Professor at Toulouse Institute of Mathematics, and Scientific Director of HCFIM)

Computer sessions will be animated by CNRS research engineer Thibault Laurent

**Detailed description of the courses**

Course: SCORING (Christine Thomas-Agnan)

Part I: Introduction

- What is scoring ?

- Background on linear regression models

- Generalized linear regression models

Part II: Logistic regression

- Fundamental assumption – Odds

- Estimation and interpretation of coefficients

- Tests

- Goodness of fit: sensibility, specificity and ROC curves

Part III: Scorecard development

- Data preparation (variable treatment)

- Characteristic selection

- Scorecard calibration

- Reject inference

It is important for this course to already know the background on ordinary linear regression models

Bibliography:

1- Background on linear regression models: any book on that topic (you may tell me what you have and I can advice you then on what to read)

2- Generalized Linear regression

chapters 1 and 6 of Extending the linear model with R, J.J. Faraway, Chapman \& Hall/CRC, 2006.

chapter 7 of W.N. Venables and B.D.Ripley, Modern Applied Statistics with S, 2002, Springer.

chapter 1 and 2 of Generalized additive models, an introduction with R, S. Wood, Chapman \& Hall/CRC, 2006.

chapter 2 of L. Fahrmeir and G. Tutz, Multivariate statistical modelling based on generalized linear models, Springer series in statistics, 1994.

3- Logistic regression

J.M. Hilbe, Logistic regression models, CRC Press, Chapman and Hall, 2009.

D.W. Hosmer, S. Lemeshow, Applied logistic regression, second edition, Wiley, 2000.

4- Scorecard development

R. Anderson, The credit scoring toolkit, Oxford U.P., 2007.

Thomas, Edelman and Crook, Credit scoring and its applications, SIAM, 2002.

N. Siddiqi, Credit risk scorecards, Wiley, 2006.

——–

Course: Time series applied to Finance(Anne Vanhems)

The objective of this course is to gain a working knowledge of time series and forecasting methods as applied in economics, engineering and finance. The purpose is to study techniques for drawing inferences from time series. After an appropriate family of models has been chosen, it is then possible to estimate parameters, check for goodness of fit to the data, and possibly to use the fitted model to enhance our understanding of the mechanism generating the series.

After recalling some basic notions in statistics and modeling, we will present the main time series models: ARMA, SARIMA, ARCH, GARCH

Outline of the course:

1) Introduction to Time-series Analysis and stochastic processes

2) Stationnarity of a process and ARMA modeling

3) Box-Jenkins methodology: identification, estimation and testing

4) Times series in finance and conditional heteroscedastic models: ARCH and GARCH

It is important for this course to already know the background on linear regression models, linear projection of Hilbert spaces, maximum likelihood estimation and standard testing hypothesis.

A few references:

- P.J. Brockwell and R.A. Davis:” Introduction to Time series and forecasting”, Springer Texts in Statistics, Springer

- J.D. Hamilton: “Time series analysis” , Princeton University Press

- C. Brooks: “Introductory econometrics for finance”, Cambridge University Press

- C. Gouriéroux and J. Jasiak: “Financial econometrics : problems, models, methods », Princeton Series in Finance

—–

Course: Nonparametric Models with Applications to Production Frontiers

(Michel Simioni, Toulouse School of Economics, INRA-GREMAQ)

The approach of production frontiers is an effort to define empirically an envelopment of production data. This approach is based on the conventional microecomic theory paradigm, assuming that producers optimize by no wasting resources in a systematic way, i.e. producers operate somewhere on the boundary of their production possibility sets, namely the production frontier. Empirical evidence shows that not all producers succeed in all circumstances. Hence, it is important to analyze the degree to which producers fail to optimize and the extent of departures from technical and economic efficiency. The aim of the course is thus to provide an overview of nonparametric methods used in production frontier estimation and efficiency measurement.

1.Production Frontiers and the Measurement of Efficiency

The economic model

A taxonomy of production frontier models

The nonparametric envelopment estimators:

Data Envelopment Analysis (DEA)

Free Disposal Hull (FDH)

2.Statistical Inference in Nonparametric Frontier Estimation

Statistical foundation

A summary of asymptotic results

Bootstrapping DEA and FDH Efficiency scores

3.Robust Nonparametric Frontier Estimators

A reformulation based on the probability of being dominated

Order-m partial frontiers

Order-α quantile-type frontiers

4.Explaining Efficiencies

The two-stage regression approach

Conditional efficiency measures

5.Conclusion

References:

Daraio, C., and L. Simar (2007), Advanced Robust and Nonparametric Methods in Efficiency Analysis, Springer, New-York.

Fried, H.O., Lovell, C.A.Knox, and S.S. Schmidt (2008), The Measurement of Productive Efficiency and Productivity Growth, Oxford University Press, Oxford.

Software:

Wilson, P. (2008), “FEAR 1.0: A Software Package for Frontier Efficiency Analysis with R,” Socio-Economic Planning Sciences 42, 247-254.

See http://www.clemson.edu/economcs/faculty/wilson/Software/FEAR/fear.html

——

Course: QUANTITATIVE PORTFOLIO MANAGEMENT

This course will be an overview of modern theories of porfolio management, with some applications to investing in stock markets in Vietnam.

1. Measures of risk and return

- Risk/return relationship

- Expected vs. actual return

- Variance and volatility

- Downside risk

- Value at risk

2. Pricing theories

- CAPM

- APT

- Other models

3. Portfolio theories

- Constraints and objectives

- Markowitz, Black-Litterman, etc.

- Dynamic asset allocation

4. Numerical optimization methods

- Linear and quadratic programming

- Monte-Carlo

- Heuristic optimization

- Robust optimization

5. Applications to Vietnamese stock market

- Explanatory factors

- Index tracking

- Asset allocation