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

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 enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
12
A
MAT/02 ,MAT/03
12
A
MAT/05
6
B
MAT/08
12
A
FIS/01
6
B
MAT/01
12
A
INF/01

2° Year   activated in the A.Y. 2019/2020

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
6
B
MAT/08
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
6
B
MAT/06
6
B
MAT/05
English B1
6
E
-

3° Year   activated in the A.Y. 2020/2021

ModulesCreditsTAFSSD
6
C
SECS-P/05
12
C
SECS-S/06
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Final exam
6
E
-
activated in the A.Y. 2019/2020
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
6
B
MAT/08
6
B
MAT/03
6
C
SECS-P/01
6
C
SECS-P/01
6
B
MAT/06
6
B
MAT/05
English B1
6
E
-
activated in the A.Y. 2020/2021
ModulesCreditsTAFSSD
6
C
SECS-P/05
12
C
SECS-S/06
6
B
MAT/08
6
B
MAT/09
6
B
MAT/06
Final exam
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
12
D
-
Between the years: 1°- 2°- 3°
Other activities
6
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.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Financial mathematics  (2020/2021)

Teaching code

4S00393

Academic staff

Alessandro Gnoatto, Marco Patacca

Coordinator

Alessandro Gnoatto

Credits

12

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

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

Lessons timetable MoodleMoodle Seminars 0

Learning outcomes

This course presents the basic models for the analysis and evaluation of financial operations, both under conditions of certainty and randomness. The main goal of the course is to equip the student with the ability to model and solve some basic mathematical problems, commonly encountered in the financial practice.

Program

The entire course will be available online. In addition, a number of the lessons (see the course
schedule) will be held in-class.

Part 1: classical financial mathematics - Main Reference: Scandolo

1) Basic financial operations, simple interest, interest in advance, compounding of interest, exponential regime.

2) Market rates. Some sketch of the classical theory with some warnings regarding the multiple curve phenomenon.

3) Annuities and amortization: non-elementary investment and financing, annuities with constant rates, annuities with installments following a geometric progression, amortization, common amortization clauses, amortization with viariable interest rate.

4) Choice without uncertainty: return for elementary and generic investment, choice criteria for investment and financing operations.

5) Bonds: classification, zero coupon bonds, fixed coupon bonds.

6) Term structure: yield curve, complete and incomplete markets.

7) Immunization: Maculay’s duration and convexity, immunized portfolios.

Part 2: mathematical finance in the presence of uncertainty - Main references: Föllmer Schied and Pascucci Runggaldier.

8) Probability theory refresher: probability spaces, independence, Radon-Nikodym theorem, expectation, conditional expectation, martingales, convergence of random variables.

9) Preferences and risk aversion: expected utility criterion (St. Petersburgh paradox), von Neumann Morgenstern axioms, stochastic dominance, mean variance criterion and static portfolio optimization, CAPM.

10) Arbitrage theory in one period: foundations and fundamental theorem of asset pricing, contingnt claimds, market completeness.

11) Arbitrage theory in multiperiod models: fundamental on multiperiod models, absence of arbitrage, European contingent claims, binomial model (Cox-Ross Rubinstein).

12) American contingent claims: foundataions, valuation and hedging, arbitrage free prices and replicability in general markets.

Reference texts
Author Title Publishing house Year ISBN Notes
Pascucci, A. Runggaldier, W. J. Finanza matematica. Teoria e problemi per modelli multiperiodali (Edizione 1) Springer 2009 978-8-847-01441-1
Scandolo Giacomo Matematica Finanziaria Amon 2013
Scandolo Giacomo Matematica finanziaria - Esercizi Amon 2013
Föllmer, H. Schied, A. Stochastic Finance: An Introduction in Discrete Time (Edizione 4) De Gruyter 2016 978-3-110-46344-6

Examination Methods

Two-hour written exam. The exam consists of practical and theoretical exercises, including the proof of certain claims. The exam aims to verify the student's ability to identify the correct resolution, knowledge of basic financial laws and sophisticated assessment models, and the ability to apply acquired knowledge to concrete cases in new and variable contexts. The exam aims also to assess the level of understanding of the theoretical aspects of the lecture.

The assessment methods could change according to the academic rules.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE