FINANCIAL ECONOMETRICS
Syllabus
Obiettivi Formativi
I modelli econometrici per l'analisi e la previsione dei mercati finanziari rappresentano una parte essenziale del percorso formativo in economia e finanza.
La misurazione e la previsione del rischio di mercato costituiscono i temi fondamentali del corso. La parte centrale verte sulla stima della volatilità nei mercati finanziari. Verranno introdotti i modelli di eteroschedasticità condizionata, ARCH e GARCH, e le loro estensioni per catturare il premio al rischio e le asimmetrie di comportamento della volatilità. Si passerà dunque ad esaminare i modelli di volatilità stocastica e i modelli di volatilità multivariati, che trovano fondamentale impiego nella stima della matrice di covarianza condizionata da utilizzare per la scelta ottimale del portafoglio.
Costituiscono parte integrante del corso le esercitazioni, svolte in Excel, R e Matlab, e i casi di studio.
Il corso ha i seguenti obiettivi formativi:
- conoscere le principali e più avanzate e moderne tecniche di misurazione e analisi del rischio di mercato;
- saper prevedere la volatilità delle attività finanziarie ed il Value at Risk;
- acquisire la capacità di selezionare e combinare regole predittive;
- saper trattare i dati ad alta frequenza;
- essere in grado di comunicare le principali evidenze empiriche che emergono dall’'analisi;
- svolgere analisi statistiche col il software appropriato;
- apprezzare criticamente le potenzialità e i limiti delle metodologie disponibili, acquisendo la capacità di discriminare tra di esse.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE:
Il corso tratta la logica e le metodogie fondamentali dell’analisi dei dati finanziari, che servono a misurare e prevedere il rischio.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE:
Le conoscenze acquisite vengono applicate a problemi di previsione del rischio dei titoli finanziari e alla comparazione dei metodi acquisiti. Costituiscono parte integrante del corso le esercitazioni di laboratorio che vengono svolte mediante i software R e Matlab. Gli studenti utilizzano le loro conoscenze per analizzare casi di studio, sia in laboratorio che negli esercizi individuali.
AUTONOMIA DI GIUDIZIO:
Lo studente viene stimolato a trarre conclusioni sulla validità interna ed esterna dei modelli considerati sulla base del confronto con i dati osservati. Il corso dedica molta attenzione alla comunicazione delle evidenze empiriche mediante grafici e statistiche di sintesi e sulla capacità di saper presentare le suddette evidenze a non esperti, in maniera efficace e sintetica.
ABILITÀ COMUNICATIVE:
Al fine di accertare il conseguimento di questo obiettivo formativo sono previsti compiti settimanali, il cui deliverable fondamentale è una relazione scritta che evidenzi i principali elementi interpretativi delle applicazioni. Il software utilizzato (R e Matlab) è peraltro fortemente orientato verso la comunicazione grafica delle evidenze statistiche.
Learning Objectives
Econometric models of financial markets form integral part of the curriculum in economics and finance.
The course deals with the measurement, analysis and prediction of market risk. A core component is modelling volatility via conditional heteroscedastic models, i.e. ARCH and GARCH models and their extensions. We will consider their mutlivariate extensions and their role for portfolio management, touching upon high dimensional methods for financial time series and the theory of copulae. The class of stochastic volatility models will be considered and finally, we will devote our attention to the prediction of realized volatility using long memory models.
Matlab and R illustrations for integral part of the course.
KNOWLEDGE AND UNDERSTANDING:
The course teaches essential methods for predicting volatility. It provides a solid theoretical background on econometric methods for the analysis of financial markets.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The methodologies exposed during the course are applied to real life datasets and case studies, dealing with the prediction of the volatility.
Two hours per week are dedicated to tutorials where statistical analyses are conducted in the Laboratory and implemented in Matlab and R-studio.
Students are expected to perform their statistical analyses in weekly assignments
MAKING JUDGEMENTS:
The prediction of an outcome is an informed decision based on the knowledge of covariates and antecedents. The student is expected to be able to draw conclusions on the basis of the statistical evidence and to validate those conclusions on validation or test samples drawn from the same target population.
COMMUNICATION SKILLS:
Particular attention is dedicated to the ability to communicate the statistical evidence in a systematic and synthetic way, using graphs and summaries, to a non-specialist target audience.
The software used in the tutorials is oriented towards graphical displays and visualization of data. The student is asked to report on the statistical analysis carried out for a particular purpose in the individual assignments.
LEARNING SKILLS:
Students develop their learning skills by comparing the teaching material provided by the instructor and exposed in the lectures with the readings suggested with weekly periodicity. The software tutorials and the analysis of cases studies in the assignments will help build their applied skills and their autonomous progress towards the intended learning outcomes.
Prerequisiti
Prerequisites
Programma
(Lectures 1-3)
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
(Lectures 4-7)
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices. (Lectures 8-10)
4. Copulae and tail dependence (Lecture 11)
5. Risk Measurement: Value at Risk and Expected Shortfall. (Lectures 12-14).
6. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter. (Lectures 15-16)
7. Realized volatility. Long memory. (Lectures 17-18).
Program
(Lectures 1-3)
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
(Lectures 4-7)
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices. (Lectures 8-10)
4. Copulae and tail dependence (Lecture 11)
5. Risk Measurement: Value at Risk and Expected Shortfall. (Lectures 12-14).
6. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter. (Lectures 15-16)
7. Realized volatility. Long memory. (Lectures 17-18).
Testi Adottati
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Books
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliografia
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliography
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Modalità di svolgimento
Teaching methods
Regolamento Esame
• Laboratori (Matlab, R)
L’'accertamento dei risultati dell'apprendimento viene effettuato con le seguenti modalità:
30% Compiti settimanali
70% Esame finale
Il lavoro settimanale riguarda l'elaborazione e la presentazione di casi di studio riguardante la previsione della volatilità e del value at risk di uno o più titoli finanziari. Esso mira a valutare la capacità di lavorare in gruppo, di utilizzare le conoscenze e le metodologie acquisite durante il corso, nonché la capacità di comunicare le evidenze statistiche.
L’'esame finale è una prova scritta di 2 ore che valuta l’ effettiva acquisizione parte dello studente degli obiettivi formativi e dei risultati di apprendimento attesi. Esso consta di tre domande a risposta aperta con sotto-quesiti che richiedono l'elaborazione gli elementi fondamentali della specificazione dei modelli per le serie storiche finanziarie, la stima mediante il metodo della massima verosimiglianza, la verifica empirica e la validazione predittiva. Lo studente deve saper valutare criticamente le assunzioni sottostanti alla specificazione ed essere in grado di sintetizzare le proprietà statistiche dei metodi utilizzati e di prevedere i processi sottostanti. La valutazione degli elaborati è fondata sul rigore formale, l'abilità di derivare analiticamente le conseguenze delle assunzioni fatte, la consequenzialità e la fondamentale comprensione delle tecniche. Ciascun quesito e sotto-quesito ha un numero di punti dichiarato che concorre al punteggio finale.
Il voto finale sarà espresso in trentesimi con l'articolazione che segue:
- Non idoneo: importanti carenze e/o inaccuratezze nella conoscenza e comprensione degli argomenti; limitate capacità di analisi e sintesi, frequenti generalizzazioni.
- 18-20: conoscenza e comprensione degli argomenti appena sufficiente con possibili imperfezioni; capacità di analisi sintesi e autonomia di giudizio sufficienti.
- 21-23: Conoscenza e comprensione degli argomenti routinaria; Capacità di analisi e sintesi corrette con argomentazione logica coerente.
- 24-26: Buona conoscenza e comprensione degli argomenti; buone capacità di analisi e sintesi con argomentazioni espresse in modo rigoroso.
- 27-29: Distinta conoscenza e comprensione degli argomenti completa; notevoli capacità di analisi, sintesi. Distinta autonomia di giudizio.
- 30-30L: Ottimo livello di conoscenza e comprensione degli argomenti. Notevoli capacità di analisi e di sintesi e di autonomia di giudizio. Argomentazioni espresse in modo originale.
Exam Rules
• Tutorials (12 hours)
Assessment for this course has two components
30% Four Weekly Assignments
70% Final Exam
The weekly deals with the elaboration and presentation of case studies concerning the prediction of the work of the volatility and value at risk of one or more financial securities. It aims to course the ability to work in a team, to use the knowledge and methodologies acquired while communicating, as well as the statistical evidence.
The final exam is a 2 hours written test that evaluates the learning of the program topics. Students face open questions with subquestions that test the understanding of the techniques presented throughout the course and the ability to critically assess their scope. The questions deal with the specification, estimation and validation of models of financial returns, risk and volatility, both univariate and multivariate. The students will have to prove his/her proficiency in understanding the basic assumptions that are made about the stochastic process generating the series, how the data are used to learn about the model parameters, and finally how we diagnose the external and predictive validity of the methods and models. The assessment criteria are based on mathematical rigour, ability to derive consequences from the stated assumptions, consequentiality and understanding. Main questions and items are scored according to difficulty. The score is disclosed to the students directly on the exam paper.
The final grade will be expressed in thirtieths with the following breakdown:
- Fail: significant deficiencies and/or inaccuracies in the knowledge and understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
- 18-20: barely sufficient knowledge and understanding of the topics with possible imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
- 21-23: routine knowledge and understanding of the topics; correct analytical and synthesis skills with consistent logical reasoning.
- 24-26: good knowledge and understanding of the topics; good analytical and synthesis skills with rigorously expressed arguments.
- 27-29: excellent and comprehensive knowledge and understanding of the topics; notable analytical and synthesis skills, and excellent judgment autonomy.
- 30-30L: outstanding level of knowledge and understanding of the topics; notable analytical, synthesis, and judgment autonomy skills. Arguments are expressed in an original manner.
Obiettivi Formativi
I modelli econometrici per l'analisi e la previsione dei mercati finanziari rappresentano una parte essenziale del percorso formativo in economia e finanza.
La misurazione e la previsione del rischio di mercato costituiscono i temi fondamentali del corso. La parte centrale verte sulla stima della volatilità nei mercati finanziari. Verranno introdotti i modelli di eteroschedasticità condizionata, ARCH e GARCH, e le loro estensioni per catturare il premio al rischio e le asimmetrie di comportamento della volatilità. Si passerà dunque ad esaminare i modelli di volatilità stocastica e i modelli di volatilità multivariati, che trovano fondamentale impiego nella stima della matrice di covarianza condizionata da utilizzare per la scelta ottimale del portafoglio.
Costituiscono parte integrante del corso le esercitazioni, svolte in Excel, R e Matlab, e i casi di studio.
Il corso ha i seguenti obiettivi formativi:
- conoscere le principali e più avanzate e moderne tecniche di misurazione e analisi del rischio di mercato;
- saper prevedere la volatilità delle attività finanziarie ed il Value at Risk;
- acquisire la capacità di selezionare e combinare regole predittive;
- saper trattare i dati ad alta frequenza;
- essere in grado di comunicare le principali evidenze empiriche che emergono dall’'analisi;
- svolgere analisi statistiche col il software appropriato;
- apprezzare criticamente le potenzialità e i limiti delle metodologie disponibili, acquisendo la capacità di discriminare tra di esse.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE:
Il corso tratta la logica e le metodogie fondamentali dell’analisi dei dati finanziari, che servono a misurare e prevedere il rischio.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE:
Le conoscenze acquisite vengono applicate a problemi di previsione del rischio dei titoli finanziari e alla comparazione dei metodi acquisiti. Costituiscono parte integrante del corso le esercitazioni di laboratorio che vengono svolte mediante i software R e Matlab. Gli studenti utilizzano le loro conoscenze per analizzare casi di studio, sia in laboratorio che negli esercizi individuali.
AUTONOMIA DI GIUDIZIO:
Lo studente viene stimolato a trarre conclusioni sulla validità interna ed esterna dei modelli considerati sulla base del confronto con i dati osservati. Il corso dedica molta attenzione alla comunicazione delle evidenze empiriche mediante grafici e statistiche di sintesi e sulla capacità di saper presentare le suddette evidenze a non esperti, in maniera efficace e sintetica.
ABILITÀ COMUNICATIVE:
Al fine di accertare il conseguimento di questo obiettivo formativo sono previsti compiti settimanali, il cui deliverable fondamentale è una relazione scritta che evidenzi i principali elementi interpretativi delle applicazioni. Il software utilizzato (R e Matlab) è peraltro fortemente orientato verso la comunicazione grafica delle evidenze statistiche.
Learning Objectives
Econometric models of financial markets form integral part of the curriculum in economics and finance.
The course deals with the measurement, analysis and prediction of market risk. A core component is modelling volatility via conditional heteroscedastic models, i.e. ARCH and GARCH models and their extensions. We will consider their mutlivariate extensions and their role for portfolio management, touching upon high dimensional methods for financial time series and the theory of copulae. The class of stochastic volatility models will be considered and finally, we will devote our attention to the prediction of realized volatility using long memory models.
Matlab and R illustrations for integral part of the course.
KNOWLEDGE AND UNDERSTANDING:
The course teaches essential methods for predicting volatility. It provides a solid theoretical background on econometric methods for the analysis of financial markets.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The methodologies exposed during the course are applied to real life datasets and case studies, dealing with the prediction of the volatility.
Two hours per week are dedicated to tutorials where statistical analyses are conducted in the Laboratory and implemented in Matlab and R-studio.
Students are expected to perform their statistical analyses in weekly assignments
MAKING JUDGEMENTS:
The prediction of an outcome is an informed decision based on the knowledge of covariates and antecedents. The student is expected to be able to draw conclusions on the basis of the statistical evidence and to validate those conclusions on validation or test samples drawn from the same target population.
COMMUNICATION SKILLS:
Particular attention is dedicated to the ability to communicate the statistical evidence in a systematic and synthetic way, using graphs and summaries, to a non-specialist target audience.
The software used in the tutorials is oriented towards graphical displays and visualization of data. The student is asked to report on the statistical analysis carried out for a particular purpose in the individual assignments.
LEARNING SKILLS:
Students develop their learning skills by comparing the teaching material provided by the instructor and exposed in the lectures with the readings suggested with weekly periodicity. The software tutorials and the analysis of cases studies in the assignments will help build their applied skills and their autonomous progress towards the intended learning outcomes.
Prerequisiti
Prerequisites
Programma
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices.
4 Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5 Realized volatility. Long memory.
6 Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Program
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices.
4 Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5 Realized volatility. Long memory.
6 Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Testi Adottati
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Books
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliografia
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliography
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Modalità di svolgimento
Teaching methods
Regolamento Esame
• Laboratori (Matlab, R)
L’'accertamento dei risultati dell'apprendimento viene effettuato con le seguenti modalità:
30% Compiti settimanali
70% Esame finale
Il lavoro settimanale riguarda l'elaborazione e la presentazione di casi di studio riguardante la previsione della volatilità e del value at risk di uno o più titoli finanziari. Esso mira a valutare la capacità di lavorare in gruppo, di utilizzare le conoscenze e le metodologie acquisite durante il corso, nonché la capacità di comunicare le evidenze statistiche.
L’'esame finale è una prova scritta di 2 ore che valuta l’ effettiva acquisizione parte dello studente degli obiettivi formativi e dei risultati di apprendimento attesi. Esso consta di tre domande a risposta aperta con sotto-quesiti che richiedono l'elaborazione gli elementi fondamentali della specificazione dei modelli per le serie storiche finanziarie, la stima mediante il metodo della massima verosimiglianza, la verifica empirica e la validazione predittiva. Lo studente deve saper valutare criticamente le assunzioni sottostanti alla specificazione ed essere in grado di sintetizzare le proprietà statistiche dei metodi utilizzati e di prevedere i processi sottostanti. La valutazione degli elaborati è fondata sul rigore formale, l'abilità di derivare analiticamente le conseguenze delle assunzioni fatte, la consequenzialità e la fondamentale comprensione delle tecniche. Ciascun quesito e sotto-quesito ha un numero di punti dichiarato che concorre al punteggio finale.
Exam Rules
• Tutorials (12 hours)
Assessment for this course has two components
30% Four Weekly Assignments
70% Final Exam
The weekly deals with the elaboration and presentation of case studies concerning the prediction of the work of the volatility and value at risk of one or more financial securities. It aims to course the ability to work in a team, to use the knowledge and methodologies acquired while communicating, as well as the statistical evidence.
The final exam is a 2 hours written test that evaluates the learning of the program topics. Students face open questions with subquestions that test the understanding of the techniques presented throughout the course and the ability to critically assess their scope. The questions deal with the specification, estimation and validation of models of financial returns, risk and volatility, both univariate and multivariate. The students will have to prove his/her proficiency in understanding the basic assumptions that are made about the stochastic process generating the series, how the data are used to learn about the model parameters, and finally how we diagnose the external and predictive validity of the methods and models. The assessment criteria are based on mathematical rigour, ability to derive consequences from the stated assumptions, consequentiality and understanding. Main questions and items are scored according to difficulty. The score is disclosed to the students directly on the exam paper.
Obiettivi Formativi
I modelli econometrici per l'analisi e la previsione dei mercati finanziari rappresentano una parte essenziale del percorso formativo in economia e finanza.
La misurazione e la previsione del rischio di mercato costituiscono i temi fondamentali del corso. La parte centrale verte sulla stima della volatilità nei mercati finanziari. Verranno introdotti i modelli di eteroschedasticità condizionata, ARCH e GARCH, e le loro estensioni per catturare il premio al rischio e le asimmetrie di comportamento della volatilità. Si passerà dunque ad esaminare i modelli di volatilità stocastica e i modelli di volatilità multivariati, che trovano fondamentale impiego nella stima della matrice di covarianza condizionata da utilizzare per la scelta ottimale del portafoglio.
Costituiscono parte integrante del corso le esercitazioni, svolte in Excel, R e Matlab, e i casi di studio.
Il corso ha i seguenti obiettivi formativi:
- conoscere le principali e più avanzate e moderne tecniche di misurazione e analisi del rischio di mercato;
- saper prevedere la volatilità delle attività finanziarie ed il Value at Risk;
- acquisire la capacità di selezionare e combinare regole predittive;
- saper trattare i dati ad alta frequenza;
- essere in grado di comunicare le principali evidenze empiriche che emergono dall’'analisi;
- svolgere analisi statistiche col il software appropriato;
- apprezzare criticamente le potenzialità e i limiti delle metodologie disponibili, acquisendo la capacità di discriminare tra di esse.
CONOSCENZA E CAPACITÀ DI COMPRENSIONE:
Il corso tratta la logica e le metodogie fondamentali dell’analisi dei dati finanziari, che servono a misurare e prevedere il rischio.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE:
Le conoscenze acquisite vengono applicate a problemi di previsione del rischio dei titoli finanziari e alla comparazione dei metodi acquisiti. Costituiscono parte integrante del corso le esercitazioni di laboratorio che vengono svolte mediante i software R e Matlab. Gli studenti utilizzano le loro conoscenze per analizzare casi di studio, sia in laboratorio che negli esercizi individuali.
AUTONOMIA DI GIUDIZIO:
Lo studente viene stimolato a trarre conclusioni sulla validità interna ed esterna dei modelli considerati sulla base del confronto con i dati osservati. Il corso dedica molta attenzione alla comunicazione delle evidenze empiriche mediante grafici e statistiche di sintesi e sulla capacità di saper presentare le suddette evidenze a non esperti, in maniera efficace e sintetica.
ABILITÀ COMUNICATIVE:
Al fine di accertare il conseguimento di questo obiettivo formativo sono previsti compiti settimanali, il cui deliverable fondamentale è una relazione scritta che evidenzi i principali elementi interpretativi delle applicazioni. Il software utilizzato (R e Matlab) è peraltro fortemente orientato verso la comunicazione grafica delle evidenze statistiche.
Learning Objectives
Econometric models of financial markets form integral part of the curriculum in economics and finance.
The course deals with the measurement, analysis and prediction of market risk. A core component is modelling volatility via conditional heteroscedastic models, i.e. ARCH and GARCH models and their extensions. We will consider their mutlivariate extensions and their role for portfolio management, touching upon high dimensional methods for financial time series and the theory of copulae. The class of stochastic volatility models will be considered and finally, we will devote our attention to the prediction of realized volatility using long memory models.
Matlab and R illustrations for integral part of the course.
KNOWLEDGE AND UNDERSTANDING:
The course teaches essential methods for predicting volatility. It provides a solid theoretical background on econometric methods for the analysis of financial markets.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The methodologies exposed during the course are applied to real life datasets and case studies, dealing with the prediction of the volatility.
Two hours per week are dedicated to tutorials where statistical analyses are conducted in the Laboratory and implemented in Matlab and R-studio.
Students are expected to perform their statistical analyses in weekly assignments
MAKING JUDGEMENTS:
The prediction of an outcome is an informed decision based on the knowledge of covariates and antecedents. The student is expected to be able to draw conclusions on the basis of the statistical evidence and to validate those conclusions on validation or test samples drawn from the same target population.
COMMUNICATION SKILLS:
Particular attention is dedicated to the ability to communicate the statistical evidence in a systematic and synthetic way, using graphs and summaries, to a non-specialist target audience.
The software used in the tutorials is oriented towards graphical displays and visualization of data. The student is asked to report on the statistical analysis carried out for a particular purpose in the individual assignments.
LEARNING SKILLS:
Students develop their learning skills by comparing the teaching material provided by the instructor and exposed in the lectures with the readings suggested with weekly periodicity. The software tutorials and the analysis of cases studies in the assignments will help build their applied skills and their autonomous progress towards the intended learning outcomes.
Prerequisiti
Prerequisites
Programma
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices.
4 Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5 Realized volatility. Long memory.
6 Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Program
2 Volatility measurement and analysis: autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean. Generalized ARCH models, Integrated GARCH, Exponential GARCH models. GJR-GARCH, Leverage. Fat and heavy tails.
3 Multivariate GARCH models. VEC and BEKK. Conditional correlation models: constant and dynamic, CCC, DCC. Factor models: Factor GARCH, O-GARCH. Large dimensional covariance and correlation matrices.
4 Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5 Realized volatility. Long memory.
Testi Adottati
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Books
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliografia
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Bibliography
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Modalità di svolgimento
Teaching methods
Regolamento Esame
• Laboratori (Matlab, R)
L’accertamento dei risultati dell’apprendimento viene effettuato con le seguenti modalità:
30% Compiti settimanali
70% Esame finale
L'esame finale consiste in una prova scritta.
Il lavoro settimanale riguarda l’elaborazione e la presentazione di casi di studio riguardante la previsione della volatilità e del value at risk di uno o più titoli finanziari. Esso mira a valutare la capacità di lavorare in gruppo, di utilizzare le conoscenze e le metodologie acquisite durante il corso, nonché la capacità di comunicare le evidenze statistiche.
L’'esame finale è una prova scritta di 90 minuti che valuta l’apprendimento dei temi del programma.
Exam Rules
• Tutorials (12 hours)
Assessment for this course has two components
30% Four Weekly Assignments
70% Final Exam
The final exam is a written test
The weekly work deals with the elaboration and presentation of case studies concerning the prediction of the work of the volatility and value at risk of one or more financial securities. It aims to course the ability to work in a team, to use the knowledge and methodologies acquired while communicating, as well as the statistical evidence.
The final exam is a 90-minute written test that evaluates the learning of the program topics.
Updated A.Y. 2021-2022
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2021-2022
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2019-2020
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2019-2020
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2018-2019
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2018-2019
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Stochastic volatility models. Pseudo-maximum likelihood inference. State space models. The Kalman filter.
5. Realized volatility. Market microstructure noise. Long memory.
6. Risk measurement: Value at Risk and expected shortfall. Copulae and tail dependence.
Textbook references
Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
Fan J. and Yao, Q. (2017). The Elements of Financial Econometrics. Cambride University Press.
Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
Linton O. (2019). Financial Econometrics: Models and Methods. Cambridge University Press.
McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2017-2018
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Realized volatility. Market microstructure noise. Long memory.
5. Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2017-2018
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering. Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH) models: specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models, GJR GARCH.
3. Review of multivariate distribution theory. Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH. High-dimensional covariance estimation.
4. Realized volatility. Market microstructure noise. Long memory.
5. Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2016-2017
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering.
Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models.
Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH 2.4 Realized volatility.
Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2016-2017
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering.
Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models.
Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH 2.4 Realized volatility.
Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2014-2015
PROGRAMME
1. Introduction
- Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering.
- Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
- Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
- Autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
- Generalized ARCH models, Integrated GARCH, Exponential GARCH models.
- Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH 2.4 Realized volatility.
- Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.
Updated A.Y. 2014-2015
PROGRAMME
1. Introduction
Asset returns. Stylized facts: asymmetry, kurtosis and volatility clustering.
Stochastic processes: stationarity, purely random processes (white noise). Random walks and martingales.
Review of prediction theory. Optimal prediction. Forecasting with nonstationary models: exponential smoothing.
2. Volatility measurement and analysis
Autoregressive Conditional Heteroscedasticity (ARCH): model specification, properties, maximum likelihood estimation, prediction. Extensions: ARCH in mean.
Generalized ARCH models, Integrated GARCH, Exponential GARCH models.
Multivariate GARCH models. VEC and BEKK. Conditional correlation models: CCC, DCC. Factor models: Factor GARCH, O-GARCH 2.4 Realized volatility.
Risk measurement: Value at Risk and expected shortfall.
Textbook references
- Campbell, J., Lo, A. and MacKinlay, A. (1999). The Econometrics of Financial Markets. Princeton University Press: New Jersey.
- Franke, J., Haerdle, W.K. and Hafner, C.M. (2012). Statistics of Financial Markets. An Introduction. Third Edition. Springer.
- McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management, Princeton Series in Finance.
- Taylor, S. J. (2005). Asset Price Dynamics, Volatility, and Prediction. Princeton University Press.
- Tsay, R.S. (2010). Analysis of Financial Time Series, Third Edition. Wiley.