Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Master’s degree in Banking and Finance - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2025/2026
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Mathematical finance (2024/2025)
Teaching code
4S001142
Teacher
Coordinator
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Period
Secondo semestre LM dal Feb 17, 2025 al May 23, 2025.
Courses Single
Authorized
Learning objectives
The course offers an introduction to arbitrage theory and its applications to financial derivatives pricing in discrete and continuous time.
Prerequisites and basic notions
Preparatory courses: Mathematics, Financial Mathematics, Stochastic processes
Important knowledge for a successful learning: matrix calculations, linear systems, real functions of one or more real variables (in particular: continuous functions, composition of functions, partial derivatives), basic concepts of financial mathematics (interest rate, return of an investment, difference between bonds and shares of a firm), fundamental concepts of probability theory (sigma algebra, random variables, expected values, covariance, space L ^ 2 of rv, independence, conditional probabilities and expected values, equivalent probability measures, probability density, distribution function, Gaussian law, convergence in distribution, in probability, in L ^ 2, almost certain equality), basic concepts on stochastic processes (martingale, Brownian motion)
Program
1. Discrete market models
Uniperiod models: binomial and general. Multiperiod models: binomial and general.
Financial portfolios, the principle of non-arbitrage.
Derivatives: definition, examples, properties.
Absence of arbitrage.
Discrete-time martingale processes
Equivalent martingale measures and risk neutrality.
Numeraire
Replicable securities and valuation of derivatives
Completeness of the markets
The return of risky securities
The two fundamental asset pricing theorems
2. Market models in continuous time
Transition from discret to continuous times.
Geometric Brownian motion and modeling of empirical data
Risk quantification with a model
Ito Integral Ito, quadratic variation / covariation,
stochastic differential equations, characterization of martingales
Ito Lemma
Market model with n + 1 assets and m Brownian motions
Self-financing portfolios
Absence of arbitrage
Girsanov's theorem
Equivalent martingale measure
Replicability and pricing of derivatives
Completeness and EDP for the price function of a derivative
Delta hedging
Black and Scholes model
Formula for the price of call and put options
Students not attending the lectures: the examination methods are not differentiated between attending and non-attending students
Bibliography
Didactic methods
Organization of teaching activities: lessons, exercises,
Useful material on the moodle page of the course: slides of the lessons, exercises
Skills necessary for successful learning: willingness and ability to conduct logical reasoning in a rigorous way, and to motivate each step and the conclusions
Learning assessment procedures
The exam consists of two parts: the first is a Project Work that has to be completed by using the Java programming language. The mark on the project work has a weight of 30% on the final grade.
The Project Work can be completed by groups consisting of up to 4 people.
Aims of the project work are:
implement and deepen the understanding of the methods illustrated during the lecture.
improve the ability to work in teams.
The grade of the project work has unlimited validity.
Students get access to the written exam only if the project work has a positive valuation. Those who do not submit any solution will receive the mark 0/30.
The second part of the exam consists of a written exam on all topics of the lecture. The exam contain theoretical and practical exercises together with programming questions related to the Java programming language. In case the grade is greater or equal to 18, the written exam has a weight of 70% on the final mark.
Evaluation criteria
Characteristics of the expected performance. The student is required to demonstrate a critical and in-depth knowledge of the topics covered in the course. The concepts must not be exposed mechanically but in a reasoned way, connections among different parts of the program may be required and exercises which are different form the ones solved during the lessons can be proposed.
The concise but comprehensive exposure, the rigor, the direct pointing towards the core of the matter will be particularly appreciated. Vague, inaccurate, poorly justified or incorrect answers will be penalized
Criteria for the composition of the final grade
30% PW + 70% Final Exam if approved (see details in the section above)
Exam language
Italiano o inglese
