Financial Econometrics (2x18 hours)
Catherine Bruneau, Université Paris I
The course is divided into two parts: the first one, devoted to time series and the second one to econometric analysis of qualitative response models (notably LOGIT and PROBIT models), risk measures and copulas. Each time, the developments range from theory to applications, with practical implementations using R/Python (course of Quantitative Finance).
Econometrics I (18h) For both masters Finance-Technology-Data and Financial Economics
This course is devoted to times series: first, taken separately, with the treatment of non-stationarity (Unit root) and heteroskedasticity (ARCH effects), second, in a multivariate approach, with standard linear models (VAR models and VECM ones in case of cointegration) and an introduction to non-linear ones (smooth transition regression, STR). An extension is then presented to deal with learning of the dynamics of complex systems involving networks.
Course prerequisites: course on stationary and non-stationary time series, ARMA and VAR models
1.1 Integrated series & Unit root (review) (Session 1)
1.2 Introduction to ARCH models (Session 2)
1.3 Introduction to non-linear models: the case of STR models (Session 3)
1.4 Multivariate systems (Session 4&5)
VAR models (review)
Cointegration and VEC models
1.5 Dynamic networks including VAR models (Session 6)
Ahelegbey, D.F., Billio, M., and R. Casarin, 2015, Bayesian Graphical Models for Structural Vector Autoregressive Processes,” Journal of Applied Econometrics.
Banerjee, Dolado, Galbraith et Hendry, 1993, Cointegration, Error Correction and the Econometric Analysis of Non-stationary Data, Oxford.
Engle, R.F. and D.L McFaden, ed. Handbook of Econometrics, vol.4, pp.2843-2915.
Engle, R.F. 1982 , Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation , Econometrica , Vol. 50, No. 4 (Jul., 1982), pp. 987-1007.
Gonzalez-Rivera, G., 1998, Smooth-Transition GARCH Models, in Studies in Nonlinear Dynamics and Econometrics, Quarterly Journal Volume 3, Number 2, The MIT Press.
Granger, C. W. and T. Teräsvirta, 1993, Modelling non-linear economic relationships, Oxford University Press.
Hamilton, J. « Time Series Analysis », Princeton University Press.
Luis M. Lopez-Ramos, L.M., Romero, D. Zaman, B. and B. Beferull-Lozano, 2018, Dynamic Network identification from non-stationarity vector autoregressive time series, https://arxiv.org/abs/1807.02013, Cornwell University Library.
Lütkepohl, H., 1990, Introduction to Multiple Time Series Analysis," Springer Verlag, New-York.
Teräsvirta, T., 1996, « Modelling economic relationships with smooth transition regressions Handbook of Applied Economic Statistics, edited by David Giles and Aman Ullah.
UNIT ROOT TESTS https://faculty.washington.edu/ezivot/econ584/notes/unitroot.pdf
COINTEGRATION Lecture: Introduction to Cointegration - Applied Econometricsstaff.utia.cas.cz/barunik/files/appliedecono/Lecture7.pdf
ARCH-TYPE MODELS Introduction to ARCH Models — arch 4.4.1+9.g0c6b035 documentation
B. Financial Econometrics II (18h) For master Finance-Technology-Data onlly
This course addresses three main issues:
- Credit scoring with the classical PROBIT and LOGIT models, extended in order to deal with big data by using machine learning and neural networks
- Risk measures (Value at Risk and Expected shortfall), first, with their standard use for regulation purposes and, second, in connection with networks to capture systemic risk
- Copulas with applications to portfolio management and extensions with Bayesian networks to deal with high dimensional systems, notably to assess contagion of extreme risks.
Course prerequisites: Basic knowledges in probability, statistics, networks.
1. Qualitative response models (2 sessions)
1.1 Standard econometric approach (PROBIT and LOGIT models)
1.2 Neural networks and credit scoring with Perceptron convergence procedure and Backpropagation Learning Algorithm.
Bart, 2013, Using neural networks for credit scoring: a simple example,
Comelli, F., 2014, Comparing the Performance of Logit and Probit Early Warning Systems for Currency Crises in Emerging Market Economies , IMF working Paper WP/14/65.
Halloran, S.O Lecture 9: Logit/Probit
Moore, C. « An Introduction to Logistic and Probit Regression Models »
Tam, K.Y. and M. Y. Kiang 1992, MANAGERIAL APPLICATIONS OF NEURAL NETWORKS: THE CASE OF BANK FAILURE PREDICTIONS », Management Science, Vol. 38, N° 7.
2. Risk measures (2 sessions)
2.1 Value at risk
2.2 Expected shortfall
2.3 Coherent measures
2.4 Systemic risk measures for Network models
Jorion, P., 2007, Value at Risk: The New Benchmark for Managing Financial Risk, McGraw Hill.
McNeil, A. J. Frey, R. and P. Embrechts, 2005, Quantitative Risk Management: Concepts, Techniques and Tools., Princeton University Press.
Silva, T.C., Guerra, S. M., da Silva, M.A. and B. M. Tabak, Measuring Systemic Risk under Monetary Policy Shocks: a network approach
CRAN - Package NetworkRiskMeasures
3. Copulas’ theory (2 sessions)
4.2 Copulas and Machine learning
Bouyé, E. 2000, Copulas for Finance A Reading Guide and Some Applications », www.thierry-roncalli.com/download/copula-survey.pdf
Elidan, G., 2010, Copula Bayesian networks. In: Neural Info. Processing Systems (NIPS.)
Elidan, G., 2010, Inference-less density estimation using copula bayesian networks, in « Uncertainty in Artificial Intelligence (UAI) » . Rachev, S.T., Stein, M. and Sun, W. , Copula Concepts in Financial Markets - KIT statistik.econ.kit.edu/.../Copula_Concepts_in_Financial_Markets
Segers, J., 2013, Copulas: An Introduction I - Fundamentals - Columbia University