Quantitative Finance and Insurance

NUMERICAL AND STATISTICAL METHODS FOR FINANCE

NUMERICAL AND STATISTICAL METHODS FOR FINANCE

Academic year 2019/2020

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Support activities
• Program
• Suggested textbooks and readings
• Teaching tools

Course objectives

Ability to solve, through the use of simulation tools, some standard problems in probability and statistical inference. Ability to apply statistical concepts and statistical techniques with respect to the point estimation, hyphotesis testing and confidence sets. Ability to the code with the language R/Matlab and to use some of its main packages.

Results of learning outcomes

Knowledge and understanding
Advances knowledge of statistical modeling via point estimation, hypothesis testing and confidence intervals; basic knowlegde of Monte Carlo simulation techniques for statistical models; basic knowlegde of the language R/Matlab.

Applying knowledge and understanding
Ability to convert various problems of practical interest into statistical models and make inference on it; ability to implement a Monte Carlo simulation of a statistical model using the language R/Matlab.

Making judgements
Students will be able to discern the different aspects of statistical modeling and of  Monte Carlo simulation with the language R/Matlab.

Communication skills
Students will properly use statistical and probabilistic language arising from the classical statistics and Monte Carlo simulation; students will properly use the language R/Matlab.

Learning skills
The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of statistical modeling and Monte Carlo simulation using the language R/Matlab.

Course delivery

With regards to statistics, lectures are devoted to the theorerical aspects of statistical inference based on the likelihood function. This consists in 48 hours which include 8 hours devoted to exercises; exercises will be assigned during these lectures.

With regards to simulation, lectures are mainly devoted to the theory of Monte Carlo simulation. This course is  48 hours long (taught classes) with the following subdivision: 18 hours devoted to theory and method; 8 hours of exercises; 12 hours of practical sessions on the computer with the language R/Matlab; exercises will be assigned during the course

Learning assessment methods

During the Covid-19 emergency the learning assessment method consists in a written exam with video surveillance on Webex.

With regards to statistics, the exam consists of three parts

1) an exercise on the topics (probability) presented during the preliminary course taught by Cecilia Scarinzi; the maximum score for the excercise is 2/30

2) a question requiring a formal discussion of one of the main topics of statistical infence based on the likelihood function; the maximum score for this question is 22/30

3) an exercise on the topics (statistics) presented during the course; the maximum score for the excercise is 9/30

With regards to simulation, the exam consists of four/five exercises on the topics of transformations of random variables and simulation/integration. Examples and exercises shown during the course are exam-like-exercises. Exercises can require to draft an R-script.

Support activities

No extra activities.

Program

1. Statistics: The module deals with some key themes of the theory of statistical inference, with emphasis on the role of the likelihood function. Topics include

• Random samples and their distributions, the statistical model, the likelihood function, exponential family.
• Sufficient statistics and minimal sufficient statistics, finite properties for estimators, asymptotic properties for estimators, methods for evaluating estimators.
• Methods for constructing point estimators: method of moments and generalizations, method of the least square errors, method of maximum likelihood, methods of minimum distance. 
• Hypothesis testing: probabilistic structure of hypothesis testing, Neyman-Pearson lemma, likelihood ration tests, asymptotic tests, confidence sets; nonparametric tests

2 Simulation: this module aims at introducing the students with computational statistics methods. The program includes some computationally intensive methods in statistics, such as Monte Carlo methods, bootstrap, and permutation tests. An important part of the module will be devoted to practicals. All the methods discussed during the course will be will be implemented in the R software.

Topics includes:

1. Probability: • Cifarelli, D.M. (1998). Introduzione al cacolo delle probabilità. McGraw-Hill; • Baldi, P. (2011). Calcolo della probabilità. McGraw-Hill; • Grimmett, G. and Welsh, D. (2014). Probability: an introduction. Oxford University Press.

2. Statistics: • Azzalini, A. (1996). Statistical inference based on the likelihood function. Chapmal and Hall/CRC; • Casella, G. and Berger, R. (2001). Statistical inference. Cengage Learning Press.

3. Simulation: • Rizzo, M.L. (2015). Statistical Computing with R  (Second Edtion). Chapman & Hall/CRC The R Series; • Ross. S.M. (2006). Simulation 4th edition. Academic Press. • Jones, O., Maillardet, R. and Robinson A. (2009). Introduction to scientific programming and simulation usig R. Chapman and Hall/CRC.

Class schedule

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums