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.

A.A. 2020/2021

Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

Academic calendar

Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Definition of lesson periods
Period From To
I semestre Oct 1, 2020 Jan 29, 2021
II semestre Mar 1, 2021 Jun 11, 2021
Exam sessions
Session From To
Sessione invernale d'esame Feb 1, 2021 Feb 26, 2021
Sessione estiva d'esame Jun 14, 2021 Jul 30, 2021
Sessione autunnale d'esame Sep 1, 2021 Sep 30, 2021
Degree sessions
Session From To
Sessione di laurea estiva Jul 22, 2021 Jul 22, 2021
Sessione di laurea autunnale Oct 14, 2021 Oct 14, 2021
Sessione di laurea invernale Mar 16, 2022 Mar 16, 2022
Holidays
Period From To
Festa dell'Immacolata Dec 8, 2020 Dec 8, 2020
Vacanze Natalizie Dec 24, 2020 Jan 3, 2021
Vacanze Pasquali Apr 2, 2021 Apr 5, 2021
Festa del Santo Patrono May 21, 2021 May 21, 2021
Festa della Repubblica Jun 2, 2021 Jun 2, 2021
Vacanze estive Aug 9, 2021 Aug 15, 2021

Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

Exam calendar

Should you have any doubts or questions, please check the Enrolment FAQs

Academic staff

A B C D F G L M O R S

Albi Giacomo

giacomo.albi@univr.it +39 045 802 7913

Baldo Sisto

sisto.baldo@univr.it 045 802 7935

Bos Leonard Peter

leonardpeter.bos@univr.it +39 045 802 7987

Caliari Marco

marco.caliari@univr.it +39 045 802 7904

Castellini Alberto

alberto.castellini@univr.it +39 045 802 7908

Cubico Serena

serena.cubico@univr.it 045 802 8132

Dai Pra Paolo

paolo.daipra@univr.it +39 0458027093

Daldosso Nicola

nicola.daldosso@univr.it +39 045 8027076 - 7828 (laboratorio)

Delledonne Massimo

massimo.delledonne@univr.it 045 802 7962; Lab: 045 802 7058

Dipasquale Federico Luigi

federicoluigi.dipasquale@univr.it

Di Persio Luca

luca.dipersio@univr.it +39 045 802 7968

Favretto Giuseppe

giuseppe.favretto@univr.it +39 045 802 8749 - 8748

Gregorio Enrico

Enrico.Gregorio@univr.it 045 802 7937

Mantese Francesca

francesca.mantese@univr.it +39 045 802 7978

Marigonda Antonio

antonio.marigonda@univr.it +39 045 802 7809

Mattiolo Davide

davide.mattiolo@univr.it

Mazzuoccolo Giuseppe

giuseppe.mazzuoccolo@univr.it +39 0458027838

Monti Francesca

francesca.monti@univr.it 045 802 7910

Orlandi Giandomenico

giandomenico.orlandi at univr.it 045 802 7986

Rapa Alessandro

alessandro.rapa@univr.it

Rizzi Romeo

romeo.rizzi@univr.it +39 045 8027088

Rubio Y Degrassi Lleonard

lleonard.rubioydegrassi@univr.it

Sala Pietro

pietro.sala@univr.it 0458027850

Sansonetto Nicola

nicola.sansonetto@univr.it 049-8027932

Schiavi Simona

simona.schiavi@univr.it +39 045 802 7803

Schuster Peter Michael

peter.schuster@univr.it +39 045 802 7029

Segala Roberto

roberto.segala@univr.it 045 802 7997

Solitro Ugo

ugo.solitro@univr.it +39 045 802 7977

Study Plan

The 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 enrolment year.

CURRICULUM TIPO:
ModulesCreditsTAFSSD
ModulesCreditsTAFSSD
6
B
(MAT/05)
Final exam
32
E
-

1° Year

ModulesCreditsTAFSSD

2° Year

ModulesCreditsTAFSSD
6
B
(MAT/05)
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°1 module between the following
Between the years: 1°- 2°1 module between the following
Between the years: 1°- 2°
Between the years: 1°- 2°
Other activities
4
F
-

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.




SPlacements in companies, public or private institutions and professional associations

Teaching code

4S001109

Coordinatore

Luca Di Persio

Credits

6

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Language

English en

Period

I semestre dal Oct 1, 2020 al Jan 29, 2021.

Learning outcomes

The Mathematical Finance course for the internationalized Master's Degree ( completely taught in English) aims to introduce the main concepts of discrete as well as continuous time, stochastic approach to the theory of modern financial markets. In particular, the fundamental purpose of the course is to provide the mathematical tools characterizing the setting of Itȏ stochastic calculus for the determination, the study and the analysis of models for options, interest rates models, financial derivatives, etc., determined by stochastic differential equations driven by Brownian motion and/or impulsive random noises. Basic ingredients are the foundation of the theory of continuous-time martingale, Girsanov theorems and the Feynman–Kac theorem and their applications to the theory of option pricing with specific examples in equities, also considering path-dependent options, and within the framework of interest rates models. Great attention will be also given to the practical study and realisation of concrete models characterising the modern approach to both the risk managment and option pricing frameworks, also by mean of numerical computations and computer oriented lessons. It is important to emphasize how the Stochastic Systems course is organized in such a way that students can concretely complete and further develop their own: °ability to establish profound connections with non-mathematical disciplines, both in terms of motivation of mathematical research and of the application of the results of such surveys; ° capacity of analysis, synthesis and abstraction; ° specific computational and computer skills; ° ability to understand texts, even advanced, of Mathematics in general and Applied Mathematics in particular; • ability to develop mathematical models for physical and natural sciences, while being able to analyze its limits and actual applicability, even from a computational point of view; ° skills concerning how to develop mathematical and statistical models for the economy and financial markets; ° capacity to extract qualitative information from quantitative data; ° knowledge of programming languages or specific software.

Program

[1] Stochastic analysis: basics

Basics on stochastic processes
Stochastic processes: main examples in discrete and continuous time
Stochastic integration
The Itô-Döblin lemma
SDEs: basics with examples ( e.g.: the linear case, multiplicative noise case)
Solution of SDEs as Markov processes
Feynman-Kac formula
Girsanov theorem
Stochastic control: basics with examples (e.g.: dynamic programming principle, Pontryagin maximum principle)

[2] Discrete time models
Contingent claims, value process, hedging strategies, completeness, arbitrage
Fundamental theorems of Asset Pricing (in discrete time)
Binomial trees
Random walk and pricing
Black and Scholes formula ( derived by binomial trees analysis )


[3] Brownian Motion (BM)
review of the main properties of the BM: filtration generated by BM, martingale property, quadratic variation, volatility, reflection properties, etc.

[4] Continuous time models
Black-Scholes-Merton Equation
Evolution of Portfolio/Option Values
Sensitivity analysis
The Martingale approach
Hedging and replicating strategies
Equity market models
Siegel paradox
Packages and Exotic options


[5] Interest rates models
Markovian Models of the Short Rate
Merton model
Stochastic interest rate for the Black and Scholes model
Hedging portfolio
Change of numeraire ( also under multiple risk sources )
Caps, floors, collars
Interest rates models
Vasicek model
Cox-Ingersoll-Ross model
Forward rates modelling
Arbitrage models for term structure
Heath-Jarrow-Morton framework
The Hull-White extended Vasicek model

[6] Portfolio choice and Asset Pricing
Bachelier and Samuelson models
Utility functions
The Merton problem ( value and static programming approach)
Utility maximization problem

[7] Miscellanea
Valuation of Options in Gaussian Models
Forward LIBORs
Swap rates modelling
Mean Field Games approach to systems of interacting financial agents
Calibration for Interest Rate models
Stochastic control and financial models (e.g.: the Heston model case)
Stochastic volatility models and applications
Polynomial/asyntotic espansions for financial models
SDEs on networks with financial applications

Bibliografia

Reference texts
Author Title Publishing house Year ISBN Notes
I. Karatzas and S. Shreve Brownian motion and stochastic calculus  
R. Cont, P. Tankov Financial Modelling With Jump Processes Chapman and Hall, CRC Press 2003
D. Lamberton and B. Lapeyre Introduction to Stochastic Calculus Applied to Finance  
A. F. McNeil, R. Frey, P. Embrechts Quantitative Risk Management:Concepts, Techniques and Tools Princeton University Press 2015
S. E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models Springer, New York 2004
S. E. Shreve Stochastic Calculus for Finance I: The Binomial Asset Pricing Model Springer, New York 2004
J. -P. Bouchaud, M. Potter Theory of Financial Risk - From Statistical Physics to Risk Management University Press, Cambridge 2000

Examination Methods

Oral exam with written exercises:
the exam is based on open questions as well as on the resolution of written exercises to be solved during the test itself
and/or on questions and exercises based on specific projects presented during the exam and previously agreed with the professor. Questions, open-ended and exercises, aim at verify both the knowledge about arguments developed within the course, the solution of concrete problems belonging to Mathematical Finance, and to the acquired acquaintance of associated tools of stochastic analysis.

Type D and Type F activities

I semestre From 10/1/20 To 1/29/21
years Modules TAF Teacher
1° 2° Algorithms D Roberto Segala (Coordinatore)
1° 2° Scientific knowledge and active learning strategies F Francesca Monti (Coordinatore)
1° 2° Genetics D Massimo Delledonne (Coordinatore)
1° 2° History and Didactics of Geology D Guido Gonzato (Coordinatore)
II semestre From 3/1/21 To 6/11/21
years Modules TAF Teacher
1° 2° Advanced topics in financial engineering F Luca Di Persio (Coordinatore)
1° 2° Algorithms D Roberto Segala (Coordinatore)
1° 2° Python programming language D Vittoria Cozza (Coordinatore)
1° 2° Organization Studies D Giuseppe Favretto (Coordinatore)
List of courses with unassigned period
years Modules TAF Teacher
1° 2° ECMI modelling week F Not yet assigned
1° 2° ESA Summer of code in space (SOCIS) F Not yet assigned
1° 2° Google summer of code (GSOC) F Not yet assigned
1° 2° Introduzione all'analisi non standard F Sisto Baldo
1° 2° C Programming Language D Pietro Sala (Coordinatore)
1° 2° LaTeX Language D Enrico Gregorio (Coordinatore)
1° 2° Mathematics mini courses F Marco Caliari (Coordinatore)

Career prospects


Module/Programme news

News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details.

Attendance

As stated in point 25 of the Teaching Regulations for the A.Y. 2021/2022, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Please refer to the Crisis Unit's latest updates for the mode of teaching.

Graduation

Attachments

List of theses and work experience proposals

theses proposals Research area
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Hamilton-Jacobi theories, including dynamic programming
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Manifolds
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Optimality conditions
Formule di rappresentazione per gradienti generalizzati Mathematics - Analysis
Formule di rappresentazione per gradienti generalizzati Mathematics - Mathematics
Mathematics Bachelor and Master thesis titles Various topics
Stage Research area
Internship proposals for students in mathematics Various topics

Gestione carriere


Double degree

The University of Verona, through a network of agreements with foreign universities, offers international courses that enable students to gain a Double/Joint degree at the time of graduation. Indeed, students enrolled in a Double/Joint degree programme will be able to obtain both the degree of the University of Verona and the degree issued by the Partner University abroad - where they are expected to attend part of the programme -, in the time it normally takes to gain a common Master’s degree. The institutions concerned shall ensure that both degrees are recognised in the two countries.

Places on these programmes are limited, and admissions and any applicable grants are subject to applicants being selected in a specific Call for applications.

The latest Call for applications for Double/Joint Degrees at the University of Verona is available now!


Alternative learning activities

In order to make the study path more flexible, it is possible to request the substitution of some modules with others of the same course of study in Mathematics at the University of Verona (if the educational objectives of the modules to be substituted have already been achieved in the previous career), or with others of the course of study in Mathematics at the University of Trento.

Attachments


Further services

I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.