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. 2015/2016

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, 2015 Jan 29, 2016
II semestre Mar 1, 2016 Jun 10, 2016
Exam sessions
Session From To
Sessione straordinaria Appelli d'esame Feb 1, 2016 Feb 29, 2016
Sessione estiva Appelli d'esame Jun 13, 2016 Jul 29, 2016
Sessione autunnale Appelli d'esame Sep 1, 2016 Sep 30, 2016
Degree sessions
Session From To
Sess. autun. App. di Laurea Oct 12, 2015 Oct 12, 2015
Sess. invern. App. di Laurea Mar 15, 2016 Mar 15, 2016
Sess. estiva App. di Laurea Jul 19, 2016 Jul 19, 2016
Sess. autun. 2016 App. di Laurea Oct 11, 2016 Oct 11, 2016
Sess. invern. 2017 App. di Laurea Mar 16, 2017 Mar 16, 2017
Holidays
Period From To
Festività dell'Immacolata Concezione Dec 8, 2015 Dec 8, 2015
Vacanze di Natale Dec 23, 2015 Jan 6, 2016
Vacanze Pasquali Mar 24, 2016 Mar 29, 2016
Anniversario della Liberazione Apr 25, 2016 Apr 25, 2016
Festa del S. Patrono S. Zeno May 21, 2016 May 21, 2016
Festa della Repubblica Jun 2, 2016 Jun 2, 2016
Vacanze estive Aug 8, 2016 Aug 15, 2016

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 G M O R S Z

Angeleri Lidia

lidia.angeleri@univr.it 045 802 7911

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

Daldosso Nicola

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

Di Persio Luca

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

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

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

Rizzi Romeo

romeo.rizzi@univr.it +39 045 8027088

Schuster Peter Michael

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

Solitro Ugo

ugo.solitro@univr.it +39 045 802 7977
Marco Squassina,  January 5, 2014

Squassina Marco

marco.squassina@univr.it +39 045 802 7913

Zampieri Gaetano

gaetano.zampieri@univr.it +39 045 8027979

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
6
B
(MAT/05)

2° Year

ModulesCreditsTAFSSD
6
B
(MAT/05)
Modules Credits TAF SSD
Between the years: 1°- 2°One course to be chosen among the following
Between the years: 1°- 2°
Between the years: 1°- 2°
Other activitites
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

Credits

6

Coordinatore

Luca Di Persio

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Language

English

The teaching is organized as follows:

Esercitazioni

Credits

1

Period

I semestre

Academic staff

Michele Bonollo

Teoria 1

Credits

2

Period

I semestre

Academic staff

Luca Di Persio

Teoria 2

Credits

3

Period

I semestre

Academic staff

Michele Bonollo

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Learning outcomes

The Mathematical Finance course for the internationalized Master's Degree (delivered completely in English) aims to introduce the main concepts of stochastic discrete and continuous time part of the modern theory of 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 and / or interest rates determined by stochastic differential equations driven by Brownian motion. Basic ingredients are the foundation of the theory of continuous-time martingale, Girsanov theorems and the Faynman-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.

Program

Discrete time models
• Contingent claims, value process, hedging strategies, completeness, arbitrage
• Fundamental theorems of Asset Pricing (in discrete time)

The Binomial model for Assset Pricing
• One period / multiperiod Binomial model
• A Random Walk (RW) interlude (scaled RW, symmetric RW, martingale property and quadratic variation of the symmetric RW, limiting distribution)
• Derivation of the Black-Scholes formula (continuous-time limit)

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

Stochastic Calculus
• Itȏ integral
• Itȏ-Döblin formula
• Black-Scholes-Merton Equation
• Evolution of Portfolio/Option Values
• Solution to the Black-Scholes-Merton Equation
• Sensitivity analysis

Risk-Neutral Pricing
• Risk-Neutral Measure and Girsanov's Theorem
• Pricing under the Risk-Neutral Measure
• Fundamental Theorems of Asset Pricing
• Existence/uniqueness of the Risk-Neutral Measure
• Dividend/continuously-Paying
• Forwards and Futures

Binomial model: numerical approaches
•Parameters for the binomial model
•The binomial model implementation
•Hedging for the binomial model


Black and Scholes: review and numerical implementation(s)
•The Itȏ-Döblin formula: a review
•Pricing Hedging and Risk for the Plain Vanilla Options
•Delta-Vega-Gamma Approsimations: Numerical Experiments
•Morte Carlo pricing princples: some easy cases
•The leverage effect of an option


Functionals of the Brownian motion and geometric Brownian motion
•The first hittting time distribution and density
•The occupation time and the Takacs formula
•The Local time definition, related quantities and density


Applications of the BM functional to the option pricing
•Barrier Options
•Digital Options
•Accumulators Options
•Implementations in VBA and MATHCAD


The Asian style options
•Impact of the fixing frequency
•Monte Carlo Evaluations
•Monte Carlo accuracy: how to build a confidence level for the pricer
•The Matching moment method (MMM): principles
•The MMM implementation for the Asian option


Advanced probabilistic tools for exotic options
•The best-of and the worst-of options.
•The worst and the best distribution for uncorrelated basket
•Extension to correlated basket


Credit Risk
•Default definition
•The relevant parameters for the credit risk: PD, EAD, LGD
•The credit portfolio Loss
•The Basel Gordy model
•A Monte Carlo framework for the loss distribution

Paolo Guasoni mini course: the didactic material concerning this part is the subset of the following topics that have been concretely treated during the 8 hours mini course given by Prof. Paolo Guasoni (DCU-Dublin) [ ask to Prof. Di Persio for further infos] :

1. Classical Theory.
The discussion starts with a review of the Merton consumption-investment problem with constant investment
opportunities, and with its asset-pricing counterpart, the Lucas model.
2. Long-run, state variables, and stochastic investment opportunities.
The discussion starts with the general model of a market with several state variables, the objectives of
equivalent safe rate and equivalent annuity, their corresponding HJB equations, and nite-horizon bounds.
Applications to models of return predictability and stochastic volatility conclude. [4].
3. Transaction Costs.
A market with transaction costs and constant investment opportunities is equivalent to another market,
found explicitly, in which investment opportunities are stochastic, but transaction costs absent. [1].
4. Price Impact.
If trading speed a ects execution prices, portfolio weights are no longer controls, but state variables. The
optimal trading speed follows an autonomous di usion process, interpreted as trading volume. Short and
levered positions are endogenously banned by this friction. [5]
5. High-water marks and hedge-fund fees.
In a model of hedge fund compensation, the state variable is the ratio between the fund's assets and its
historical maximum. The long-run solution leads to a simple optimal portfolio, which shows the interplay
between fees and risk aversion. [3, 2]
6. Path-dependent Preferences and Shortfall Aversion.
A model in which the marginal utility from increases in consumption above its historical maximum is lower
than the marginal utility of marginal decreases in consumption (shortfall aversion) can explain high asset
prices and low interest rates, as well as smooth consumption with volatile wealth. [6]
References
[1] S. Gerhold, P. Guasoni, J. Muhle-Karbe, and W. Schachermayer. Transaction costs, trading volume, and the
liquidity premium. Finance and Stochastics, 18(1):1{37, 2014.
[2] P. Guasoni and J. Muhle-Karbe. Long horizons, high risk-aversion, and endogenous spreads. Mathematical
Finance, 25(4):724753, 2011.
[3] P. Guasoni and J. Obloj. The incentives of hedge fund fees and high-water-marks. Mathematical Finance,
2015, 2009.
[4] P. Guasoni and S. Robertson. Portfolios and risk premia for the long run. The Annals of Applied Probability,
22(1):239{284, 2012.
[5] P. Guasoni and M. Weber. Dynamic trading volume. Mathematical Finance, 2015. forthcoming.
[6] Paolo Guasoni, Gur Huberman, and Dan Ren. Shortfall aversion. Available at SSRN 2564704, 2015.

Examination Methods

Final Exam : the exam will consists in an oral session plus a case study developed according with prof. Michele Bonollo with respect to the following list of case studies:

#1: Stress Test of derivatives portfolios
#2: Derivatives portfolio evaluation and management
#3: Credit Portfolio Risk
#4: Exotic Options Pricing

Type D and Type F activities

Modules not yet included

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.

Gestione carriere


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

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


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!


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.