STATISTICAL MODELS AND METHODS FOR FINANCE-2

In the first period the course focuses on introducing univariate statistical techniques for estimating financial risk measures (e.g., volatility, value at risk, expected shortfall), when interest is on modeling prices and returns of financial assets.
Lectures will focus on providing a conceptual understanding of the unified nature of statistical inference in risk analysis, applying esplorative and estimation methods to analyze univariate phenomena in order to make data-based decisions.
Emphasis will be given to the correct and effective interpretation of results and to the development of critique data-based claims and decisions.
Particular attention will be devoted to the understanding of the proposed methods, both from a computational and a methodological perspective.
In the second period, the course aims to provide 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. Comprehension:
- understanding the relationship between uncertainty and risk involved in financial activities;
- understanding the main risk measures and their limitations;
- understanding the most common probabilistic univariate models and their different characteristics;
- understanding the inferential procedures based on the likelihood functions.;
- understanding the joint probabilistic modelling of multivariate random variables and the meaning of dependence and linear dependence;
- understanding the role of stochastic processes in the modelling of the temporal dynamics of financial data.

2. Applied knowledge:
- compute point and interval estimates of risk measures from univariate probabilistic model to prices and/or returns of a single asset;
- use of explorative data-analysis tools to describe the empirical distribution of the observed data;
- estimate an univariate statistical model via maximum likelihood;
- selecting the best probabilistic model, among a set of candidates, using information criteria;
- evaluating the uncertainty associated with the inferential conclusions;
- implementation skills of basic inferential precedures on univariate time series data;
- ability to interact with professionals specialised in the analysis of financial data.


3. Evaluating:
- understand and describe with rigorous jargon the main aspects of data under investigation;
- discuss the limits and benefits of the proposed statistical model in providing a representation of reality;
- take decisions among competitive models, based on the empirical evidence.

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).

The full 12 credit course programme is:
1. Risk, probability and risk measures;
2. Recall of statistical inference (estimators, point and interval estimations, hypothesis testing);
3. Tools for exploratory analysis (histogram, quantile-quantile plot);
4. Univariate distributions and main properties (location-scale families, skewness, kurtosis);
5. Random vectors;
6. Introduction to estimation based on the likelihood function;
7. Definition of stochastic process. Stationary and non stationary stochastic processes;
8. Linear time series models;
9. Introduction to ARCH and GARCH models.

Ruppert, D. (2011). Statistics and Data Analysis for Financial Engineering, Springer, 2011, ch. 1, 2, 4, 5 (5.1-5.5, 5.7, 5.10, 5.12, 5.14), 9, 18, 19 (19.1-19.2), Appendix A.

or, equivalently,

Ruppert, D. and Matteson D.S. (2015). Statistics and Data Analysis for Financial Engineering, Springer, 2011, ch. 1, 2, 4, 5 (5.1-5.5, 5.7, 5.10, 5.12, 5.14), 12, 14, 19 (19.1, 19.2, 19.4), 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 forstatistical computing. R Foundation for StatisticalComputing, Vienna, Austria. URL http://www.R-project.org/

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

The final assessment consists of a written test composed by single choice questions, exercises and theoretical: multiple choice questions aim to verify the calculation ability and the understanding of the fundamental concepts of the discipline; the exercises and open questions are intended to test the students' analytical and communication skills. Incorrect or missing answers do not give rise to any penalty. As regards the grading (how the grades will be assigned), regardless of the attending or non-attending mode:
A. scores in the 18-22 range will be awarded in case of:
- sufficient applied skills in relation to the programme;
- limited ability to manage and/or interpret probabilistic and statistical techniques;
- sufficient communication skills, especially in relation to the use of discipline-specific language;
B. scores in the 23-26 range will be awarded in the presence of:
- fair applied skills in relation to the programme;
- fair ability to manage and/or interpret probabilistic and statistical techniques;
- fair communication skills, especially in relation to the use of discipline-specific language;
C. scores in the 27-30 range will be awarded in the presence of:
- good or very good knowledge and ability to understand applied in relation to the programme;
- good or very good ability to manage and/or interpret probabilistic and statistical techniques;
- good or very good communication skills, especially in relation to the use of discipline-specific language;
D. the distincion of honors will be awarded in the presence of knowledge and ability to understand applied in reference to
program, judgment and communication skills, excellent and following the presentation of a written report on the analysis of a financial dataset.
Examples of multiple choice questions and exercises are available on Ca' Foscari Moodle elearning platform.
The exam is closed-notes and closed-book. Students are allowed to use a pocket calculator and two sides of an A4-sheet prepared by them at home.

Lecture-style instructions. Students are recommended to register to the course on Moodle platform, where they can find additional material (slides, exercises, software userguide and code, homework instructions) [https://moodle.unive.it/course/view.php?id=8096 ]

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