# STATISTICAL SCIENCES FOR FINANCE | MODELLI STATISTICI PER IL RISK MANAGEMENT

## STATISTICAL SCIENCES FOR FINANCE MODELLI STATISTICI PER IL RISK MANAGEMENT

 0222400037 DEPARTMENT OF ECONOMICS AND STATISTICS EQF7 STATISTICAL SCIENCES FOR FINANCE 2022/2023

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2014 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/03 10 60 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 GIUSEPPE STORTI T
ExamDate
MODELLI STATISTICI PER IL RISK MANAGEMEN03/04/2023 - 09:00
MODELLI STATISTICI PER IL RISK MANAGEMEN03/04/2023 - 09:00
Objectives
KNOWLEDGE AND UNDERSTANDING
THE COURSE AIMS AT PROVIDING THE STUDENTS WITH THE BASIC METHODOLOGICAL TOOLS FOR UNDERSTANDING ADVANCED QUANTITATIVE MODELS FOR THE ANALYSIS OF FINANCIAL MARKETS AND THEIR RISK STRUCTURE.
IN PARTICULAR IT IS EXPECTED THAT THE STUDENTS MASTER THE FOLLOWING NOTIONS
-KNOWLEDGE OF THE MAIN DATABASES FOR RISK MANAGEMENT APPLICATIONS
-KNOWLEDGE OF THE MAIN EX-POST VOLATILITY ESTIMATORS
-KNOWLEDGE OF THE MAIN UNIVARIATE AND MULTIVARIATE MODELS FOR FORECASTING FINANCIAL VOLATILITY
-KNOWLEDGE OF THE MAIN METHODS AND MODELS FOR FORECASTING FINANCIAL RISK MEASURES (VAR AND ES)
-KNOWLEDGE OF THE MAIN METHODS FOR BACKTESTING FINANCIAL RISK MEASURES

APPLYING KNOWLEDGE AND UNDERSTANDING
THE COURSE AIMS AT HELPING THE STUDENTS TO DEVELOP THE ABILITY OF USING ADVANCED QUANTITATIVE MODELS FOR THE ANALYSIS OF FINANCIAL MARKETS.
-IN PARTICULAR IT IS EXPECTED THAT THE STUDENTS DEVELOP THE FOLLOWING ABILITIES

-ABILITY TO IMPLEMENT INTO THE R LANGUAGE THE MAIN METHODS FOR ESTIMATION, FORECASTING AND BACKTESTING OF VOLATILITY AND THE MAIN FINANCIAL RISK MEASURES
-ABILITY TO IMPLEMENT ON REAL DATASETS THE MAIN RISK MANAGEMENT APPLICATIONS INCLUDING FORECASTING AND BACKTESTING RISK MEASURES AND PORTFOLIO OPTIMIZATION

COMMUNICATION SKILLS
ABILITY TO RIGOROUSLY PRESENT TO A SPECIALIZED AUDIENCE THE RESULTS OBTAINED FROM THE APPLICATION OF ADVANCED QUANTITATIVE MODELS TO SIMPLE FINANCIAL INSTRUMENTS AND DERIVATIVES.

MAKING JUDGEMENTS
THE STUDENTS ARE EXPECTED TO BE ABLE TO CRITICALLY CHOOSE THE MOST APPROPRIATE MODEL FOR A GIVEN CASE STUDY OF INTEREST.

LEARNING SKILLS
ABILITY TO SUCCESSFULLY ATTEND ADVANCED COURSES IN STATISTICS OF FINANCIAL MARKETS, FINANCIAL ECONOMETRICS AND MATHEMATICAL FINANCE IN MASTER OR DOCTORATE COURSES.
Prerequisites
IT IS EXPECTED THAT STUDENTS ATTENDING THE COURSE HAVE A BASIC KNOWLEDGE OF PROBABILITY AND STATISTICAL INFERENCE. IN PARTICULAR IT IS DESIRABLE THAT THE STUDENTS TAKING THE COURSE HAVE SUCCESSFULLY ATTENDED THE STOCHASTIC PROCESSES AND STATISTICAL INFERENCE COURSES DURING THE FIRST YEAR OF THEIR STUDY PLAN.
Contents
MODULE A (30 HOURS):
THIS MODULE INCLUDES LECTURES ON THE FOLLOWING TOPICS:

UNIVARIATE ANALYSIS: EFFICIENT MARKETS. MEASURING RETURNS. MEASURING VOLATILITY: DESCRIPTIVE TECHNIQUES BASED ON MOVING AVERAGES, REALIZED VOLATILITY, OTHER VOLATILITY MEASURES.

STOCHASTIC MODELS FOR THE LEVELS OF RETURNS. STOCHASTIC MODELS FOR THE VOLATILITY OF RETURNS. THE LEVERAGE EFFECT. UNIVARIATE RISK MEASURES: VAR AND L’EXPECTED SHORTFALL. BACKTESTING. DEVELOPMENT AND DISCUSSION OF CASE STUDIES USING THE R SOFTWARE.

MODULE B (30 HOURS)
THIS MODULE INCLUDES LECTURES ON THE FOLLOWING TOPICS:

MEASURING VOLATILITY IN A MULTIVARIATE SETTTING. VAR MODELS. MULTIVARIATE CONDITIONAL HETEROSKEDASTIC MODELS: 1) DYNAMIC MODELS FOR THE CONDITIONAL COVARIANCE MATRIX (DVEC, BEKK) 2) MODELS FOR CONDITIONAL CORRELATIONS (CCC, DCC). ESTIMATING VAR AND EXPECTED SHORTFALL IN A MULTIVARIATE SETTING. OTHER FINANCIAL APPLICATIONS: PORTFOLIO OPTIMIZATION AND HEDGING.
COMPLEMENTS OF MATRIX ALGEBRA, PROBABILITY THEORY AND STATISTICAL INFERENCE. DEVELOPMENT AND DISCUSSION OF CASE STUDIES USING THE R SOFTWARE.

Teaching Methods
CLASSROOM LECTURES. THE LECTURES WILL INCLUDE A DISCUSSION OF THE MAIN THEORETICAL SUBJECTS AND WILL BE COMPLEMENTED BY THE COMPUTER IMPLEMENTATION (IN R LANGUAGE) AND DISCUSSION OF REAL CASE STUDIES.

THE LECTURES WILL INCLUDE SOME COMPUTER BASED PRACTICALS INVOLVING THE ANALYSIS OF REAL DATASETS.
Verification of learning
THE SATISFACTORY ACHIEVEMENT OF THE AIMS OF THE COURSE IS ASSESSED THROUGH AN EXAM WITH MARKS OUT OF THIRTY.
THE EXAM IS BASED ON A WRITTEN TEST THAT INCLUDES NUMERICAL EXERCISES AS WELL AS THEORETICAL QUESTIONS. THE PASS MARK IS 18/30.

THE WRITTEN TEST, OF DURATION APPROXIMATELY EQUAL TO 90 MINUTES, IS AIMED AT ASSESSING THE KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE SUBJECTS INDICATED IN THE COURSE PROGRAMME, THE ABILITY TO MASTER AND APPLY THE ANALYTICAL TOOLS REQUIRED AND THE ABILITY TO APPLY THE THEORETICAL NOTIONS TAUGHT.
THE WRITTEN TEST REQUIRES I) THE SOLUTION OF NUMERICAL EXERCISES RELATED TO THE MAIN TOPICS COVERED DURING THE COURSE (E.G. ASSESSING THE STATISTICAL PROPERTIES OF ESTIMATED MODELS, FORECASTING AND BACKTESTING FINANCIAL RISK MEASURES) II) ANSWERING TO THEORETICAL QUESTIONS ON THE TOPICS INCLUDED IN THE COURSE PROGRAMME.
DURING THE TEST STUDENTS ARE NOT ALLOWED TO READ TEXTBOOKS, USE PCS, TABLETS AND MOBILE PHONES; THEY ARE ONLY ALLOWED TO USE A BASIC ELECTRONIC CALCULATOR AND THE USUAL STATISTICAL TABLES.

IN THE ASSESSMENT PROCESS, THE FOCUS WILL BE ON EVALUATING THE ABILITY TO CORRECTLY APPLY THE TAUGHT METHODS, THE RIGOUR AND CLARITY OF EXPRESSION.
Texts
FOR MODULES A AND B
TSAY, R. (2005) ANALYSIS OF FINANCIAL TIME SERIES (2ND EDITION), WILEY SERIES IN PROBABILITY AND STATISTICS (CHAPTERS 1-3-5-7-8.1-8.2.8.3-8.4-10).
FOR MODULE A
STORTI G., VITALE C. (2011) ANALISI STATISTICA DEI MERCATI MONETARI E FINANZIARI, ESI.