ID:
000516LM1
Duration (hours):
24
CFU:
3
SSD:
PROBABILITÀ E STATISTICA MATEMATICA
Located in:
PESCARA
Url:
ECONOMICS AND COMMERCE/ECONOMIA E COMMERCIO Year: 3
Year:
2026
Course Catalogue:
Overview
Date/time interval
Secondo Semestre (11/02/2027 - 18/05/2027)
Syllabus
Course Objectives
Educational objectives
The course introduces the fundamental mathematical and probabilistic tools required to model uncertainty in financial markets and to value elementary derivative securities. Through a gradual learning process, students acquire the theoretical foundations of Probability Theory and learn how to apply them to the construction of simple financial models and to the solution of quantitative problems.
The course contributes to the quantitative training of students enrolled in the Master's Degree in Economics and Finance by providing the theoretical and practical foundations required in quantitative finance, risk management and probabilistic modelling.Expected learning outcomes
By the end of the course students will be able to:Knowledge and understanding
describe the fundamental concepts of Probability Theory;
understand the properties of the main discrete and continuous probability distributions;
explain the role of probability in the construction of financial models.
Applying knowledge and understanding
compute probabilities, expectations, variances, covariances and probability distributions;
apply probabilistic methods to quantitative problems;
use binomial models for the valuation of elementary financial derivatives;
interpret financial phenomena through probabilistic models.
Making judgements
formulate quantitative financial problems;
critically assess the assumptions underlying probabilistic models;
identify the most appropriate probabilistic tools for different financial applications.
Communication skills
clearly present theoretical concepts and mathematical results;
use appropriate mathematical and probabilistic terminology;
justify the reasoning adopted in solving quantitative problems.
Learning skills
independently study advanced topics in probability and quantitative finance;
consult specialised textbooks and scientific literature;
build upon the acquired knowledge in subsequent quantitative finance courses.
The course introduces the fundamental mathematical and probabilistic tools required to model uncertainty in financial markets and to value elementary derivative securities. Through a gradual learning process, students acquire the theoretical foundations of Probability Theory and learn how to apply them to the construction of simple financial models and to the solution of quantitative problems.
The course contributes to the quantitative training of students enrolled in the Master's Degree in Economics and Finance by providing the theoretical and practical foundations required in quantitative finance, risk management and probabilistic modelling.Expected learning outcomes
By the end of the course students will be able to:Knowledge and understanding
describe the fundamental concepts of Probability Theory;
understand the properties of the main discrete and continuous probability distributions;
explain the role of probability in the construction of financial models.
Applying knowledge and understanding
compute probabilities, expectations, variances, covariances and probability distributions;
apply probabilistic methods to quantitative problems;
use binomial models for the valuation of elementary financial derivatives;
interpret financial phenomena through probabilistic models.
Making judgements
formulate quantitative financial problems;
critically assess the assumptions underlying probabilistic models;
identify the most appropriate probabilistic tools for different financial applications.
Communication skills
clearly present theoretical concepts and mathematical results;
use appropriate mathematical and probabilistic terminology;
justify the reasoning adopted in solving quantitative problems.
Learning skills
independently study advanced topics in probability and quantitative finance;
consult specialised textbooks and scientific literature;
build upon the acquired knowledge in subsequent quantitative finance courses.
Course Prerequisites
Students are expected to have a solid background in undergraduate mathematics. In particular, they should be familiar with the basic tools of mathematical analysis and linear algebra, as well as differential and integral calculus.
There are no formal prerequisites; however, the above knowledge is strongly recommended in order to successfully follow the course.
Teaching Methods
The course consists of 72 hours of classroom teaching, divided into theoretical lectures and practical sessions.
Theoretical lectures gradually introduce the fundamental concepts of Probability Theory, highlighting both their theoretical foundations and their applications to quantitative finance. Practical sessions are designed to develop students' problem-solving skills by applying probabilistic methods to quantitative problems and to the modelling of simple random phenomena.
Throughout the course, exercises, financial applications and case studies on derivative pricing and risk management will be discussed. Exercises assigned by the instructor will be reviewed in class in order to foster progressive learning and active student participation.
Teaching materials (lecture notes, slides, exercise sheets and announcements) will be made available through the University's FAD Moodle platform (https://fad.unich.it).
Additional seminars given by academic researchers or finance professionals may complement the course.
Attendance is not compulsory but is strongly recommended. The syllabus and the assessment methods are the same for attending and non-attending students.
Assessment Methods
Student assessment consists of a written examination followed by an oral examination.
The written examination consists of quantitative exercises and problems covering the topics presented during the course. Questions are graded according to their difficulty and relevance and are designed to assess students' ability to apply probabilistic methods to quantitative problems and simple financial modelling.
The written examination is graded on a 30-point scale. Students obtaining at least 18/30 are admitted to the oral examination.
The oral examination includes questions on definitions, theoretical results, examples, counterexamples and selected proofs covered during the course. It assesses students' understanding of theoretical concepts, their ability to connect different topics, their independent judgement and their command of mathematical language.
The final grade, expressed on a 30-point scale, takes into account the performance in both examinations.
Assessment will consider in particular:
mathematical correctness and logical rigour;
ability to apply probabilistic methods to quantitative problems;
understanding of theoretical concepts;
clarity of presentation and appropriate use of technical terminology;
ability to relate theoretical concepts to the financial applications discussed during the course.
Texts
Required textbooks
Sheldon Ross, Introduction to Probability Models, 13th Edition, Elsevier, 2023.
John C. Hull, Options, Futures and Other Derivatives, 11th Edition, Pearson, 2022.
Teaching material
Lecture notes, exercise sheets, slides and additional teaching material will be made available through the University's FAD Moodle platform (https://fad.unich.it) and, when appropriate, through the professor's website.
Suggested readings
Additional references may be recommended during the course for students wishing to deepen specific topics.
Contents
The course introduces the fundamental concepts of Probability Theory and develops their main applications in quantitative finance. Topics include probability spaces, combinatorial analysis, conditional probability and independence, discrete and absolutely continuous random variables, joint distributions, expectation, variance, covariance and conditional expectation. Simple probabilistic models for the valuation of financial derivatives are also presented, with particular emphasis on binomial models, risk-neutral valuation and applications to risk management. The course concludes with the Law of Large Numbers and the Central Limit Theorem, highlighting their main applications in finance.
Course Language
Italian.
More information
Office hours are held at the end of lectures and/or by appointment via email.
Office hours may also be held in English.
Course announcements, teaching materials, exercise sheets and any additional information will be published on the University's FAD Moodle platform.
Students are encouraged to regularly check both the FAD platform and their institutional email account.
Degrees
Degrees
ECONOMICS AND COMMERCE
Bachelor’s Degree
3 years
No Results Found
People
People
Docenti di ruolo di IIa fascia
No Results Found