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NUMERICAL AND STATISTICAL METHODS FOR FINANCE
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NUMERICAL AND STATISTICAL METHODS FOR FINANCE
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Academic year 2015/2016
- Course ID
- ECO0152
- Teaching staff
- Prof. Stefano Favaro (Titolare del corso)
Bernardo Nipoti (Titolare del corso) - Degree course
- Finance
Insurance and Statistics - Year
- 1° anno
- Type
- Caratterizzante
- Credits/Recognition
- 12
- Course disciplinary sector (SSD)
- SECS-S/01 - statistica
- Delivery
- Tradizionale
- Language
- Inglese
- Attendance
- Facoltativa
- Type of examination
- Scritto
- Prerequisites
- Mathematical, probabilistic and statistical tools acquired in the three-year undergraduate program. A detailed list of the required backgroud will be provided during the first lecture.
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Sommario del corso
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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.
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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.- Oggetto:
Course delivery
Main lectures are devoted to the theorerical aspects of statistical inference based on the likelihood function and Monte Carlo simulation. Exercises will be assigned during these lectures. Lecture devoted to exercises and practical sessions with the language R/Matlab are included in the course.
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Learning assessment methods
With regards to statistics, the exam consists of two parts: the first part is a formal discussion of one of the main topics of statistical infence based on the likelihood function; the second part is an exercise, typically with more than two questions. With regards to simulation, the exam consists in three parts: the first part is a forma discussion of one of the main topics on Monte Carlo simulation; the second part is an exercise, typically with more than two questions; the third part is the implementation of a simulation in the language R/Matlab.
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Support activities
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Program
1. StatisticsThe 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 evaluatingestimators.• Methods for constructing point estimators: method of moments andgeneralizations, method of the least square errors, method of maximumlikelihood, methods of minimum distance.• Hypothesis testing: probabilistic structure of hypothesis testing, Neyman-Pearson lemma, likelihood ration tests, asymptotic tests, confidence sets.2. SimulationThe module provides an introduction to simulation using the software R/Matlab.During the course the emphasis will be given to the problem of generating discrete and continuous random variables. Topics include• Functions of random variables (univariate and multivariate, discrete and continuous) and their application in generating random numbers.• Random numbers: pseudorandom number generation; using random number to evaluate integrals.• Generating discrete random variables: the inverse transform method; generating a Poisson random variable; generating Binomial random variables; the acceptance-rejection technique; generating random vector.• Generating continuous random variables: the inverse transform algorithm; the rejection method; the polar method for generating normal random variables; generating an homogeneous and nonhomogeneous Poisson process.Suggested readings and bibliography
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1. Statistics: • Grimmett, R.G. and • Azzalini, A. (1996). Statistical inference based on the likelihood function. Chapmal and Hall/CRC.
2. Simulation: • Ross. S.M. (2002) Simulation. Academic Press; • Jones, O., Maillardet, R. and Robinson A. (2009). Introduction to scientific programming and simulation usig R. Chapman and Hall/CRC.
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