STOCHASTIC MODELS FOR FINANCE

The course aims at providing the students with the basic tools for the analysis of time series oriented at prediction and risk evaluation. Multivariate probability distributions and random processes represent the theoretical foundation on which the main time series models used in the analysis of financial data are built. These foundations will be introduced in a non formal but rigorous style. Linear time series models and their main properties will be explored, with particular emphasis on the uncertainty of inferential conclusions and prediction. Some non linear models used in the estimation of volatility will also be introduced. Attention will focus mainly on applications and the development of some computing skills will be required in order to cope with the practice of financial time series analysis.

1. Knowledge and comprehension:
1.1. understanding the joint probabilistic modelling of multivariate random variables and the meaning of dependence and linear dependence;
1.2. understanding the role of stochastic processes in the modelling of the temporal dynamics of financial data.

2. Applied knowledge and comprehension skills:
2.1. implement basic inferential precedures on univariate time series data;
2.2. interpreting the output of statistical time series analysis;
2.3. ability to interact with professionals specialised in the analysis of financial data.

3. Use of independent judgement:
3.1. Understanding the meaning of statistical time series models and recognising the uncertain truthness of inferential conclusions and of statistical models themselves;
3.2. recognising the existence of changing volatility in financial time series.

Basic knowledge of calculus, probability theory and statistics at undergraduate level. In particular, the students should be familiar with the contents of chapters 3-10 of Newbold et al. (2013) (see Further references under the textbook section).

1. Multivariate probability distributions. Dependence and correlation.
2. Definition of stochastic process. Stationary and non stationary stochastic processes.
3. Linear time series models.
4. Introduction to ARCH and GARCH models.

Main textbook:
Ruppert, D. (2011): Statistics and data analysis for financial engineering. Springer
Chapters 9, 10 (10.1, 10.2 and 10.4),18 and Appendix A.
Students who have the second edition (2015) of the textbook should study Chapters 12, 13 (13.1, 13.2 and 13.5),14 and Appendix A.

Further references:
Cryer, J.D. and Chan, K. (2008): Time Series Analysis with applications in R. Springer
Newbold, P.,Carlson, W. and Thorn, B. (2013): Statistics for Business and Economics. Pearson
Tsay, R.S. (2014): An Introduction to Analysis of Financial Data with R. Wiley.
R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/

Other references will be given during the lectures and made available on Moodle platform.

The final assessment is given by a written exam consisting in open questions and exercises. Students must achieve a mark no less than 18 in order to pass the exam. A homework consisting in the analysis of a financial time series can be submitted by students who achieve a mark no less than 25 in the written exam. Such homework can increase the written exam mark of at most 4 points.
The exam evaluates the knowledge and the understanding of the main concepts and of the models presented during the course and the ability of implementing a simple analysis of financial time series data, as well as interacting with professionals working in the field of financial data analysis.

The professor will use interactive lecture-style presentations and students will be required to actively participate. Students are recommended to register to the course on Moodle platform (moodle.unive.it), where they can find additional meterial (slides, exercises, software userguide and code, homework instructions).

English

Students are invited to register to this course on the platform moodle.unive.it. The registration to the course on Moodle platform (moodle.unive.it) requires a password that will be communicated at the beginning of the course.

written