STATISTICAL METHODS FOR RISK ANALYSIS

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.

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.

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
- applications of the described methods using the statistical software R

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).

1. Risk, probability and risk measures
2. Statistical inference (point and interval estimations, hypothesis testing)
3. Tools for exploratory analysis (histogram, Kernel density estimator, quantile-quantile plot)
4. Univariate distributions and main properties (location-scale families, skewness, kurtosis)
5. Introduction to estimation based on the likelihood function

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), 7 (7.1-7.5), 19 (19.1-19.3), Appendix A.

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/ .

Newbold, P.,Varlson, W. and Thorn, B. (2013): Statistics for Business and Economics. Pearson

The final assessment consists in a 90 minute written exam including multiple choice questions and exercises, and an oral exam at the professor's discretion.

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, where they can find additional material (slides, exercises, software userguide and code, homework instructions) [https://moodle.unive.it/course/view.php?id=7108 ]

English

Students are invited to enrol to the course at the e-learning platform at the following link: https://moodle.unive.it/course/view.php?id=7108

written and oral