Training and Research
PhD Programme Courses/classes
This page shows the PhD course's training activities for the academic year 2024/2025. Further activities will be added during the year. Please check regularly for updates!
Introduction to Economics
Credits: 5
Language: English
Teacher: Roberto Ricciuti
Mathematics
Credits: 3.8
Language: English
Teacher: Andrea Mazzon
Probability
Credits: 7.5
Language: English
Teacher: Marco Minozzo
Mathematical Statistics
Credits: 5
Language: English
Teacher: Lorenzo Frattarolo, Claudia Di Caterina
Continuous Time Econometrics
Credits: 5
Language: English
Teacher: Chiara Amorino, Amorino Chiara, Cecilia Mancini
Macroeconomics I
Credits: 7.5
Language: English
Teacher: Khalid W A Shomali, Alessia Campolmi
Microeconomics 1
Credits: 7.5
Language: English
Teacher: Claudio Zoli, Martina Menon, Maurizio Malpede
Field Experiments
Credits: 1
Language: Italian
Teacher: Pol Campos
Game Theory
Credits: 5
Language: English
Teacher: Francesco De Sinopoli
Elements of Financial Risk Management
Credits: 2.5
Language: English
Teacher: Prof. Kim Christensen
Stochastic Optimization and Control
Credits: 5
Language: English
Teacher: Athena Picarelli
Financial Time Series
Credits: 5
Language: English
Teacher: Giuseppe Buccheri
Job Market Orientation
Credits: 1
Language: English
Teacher: Simone Quercia
Advice to Young Researchers
Credits: 4
Language: English
Teacher: Marco Piovesan
Finanza Matematica
Credits: 5
Language: English
Teacher: Guido Gazzani, Alessandro Gnoatto
Behavioral and Experimental Economics
Credits: 4
Language: English
Teacher: Simone Quercia, Maria Vittoria Levati, Marco Piovesan
Stochastic Processes in Finance
Credits: 5
Language: English
Teacher: Sara Svaluto Ferro
Health Economics
Credits: 4
Language: English
Teacher: Paolo Pertile
Development economics
Credits: 4
Language: English
Teacher: Federico Perali
Political Economy
Credits: 4
Language: English
Teacher: Emanuele Bracco, Roberto Ricciuti
Inequality
Credits: 4
Language: English
Teacher: Francesco Andreoli, Claudio Zoli
Quantitative research methods
Credits: 6.8
Language: English
Teacher: Luca Grassetti, Francesca Visintin, Laura Pagani
Continuous Time Econometrics (2024/2025)
Academic staff
Cecilia Mancini , Amorino Chiara, Chiara Amorino
Referent
Credits
5
Language
English
Class attendance
Free Choice
Location
VERONA
Learning objectives
The course aims to introduce the class of semimartingale processes with jumps, used in the literature as financial asset price models, and to provide tools for estimating and testing jumps in financial asset prices
Prerequisites and basic notions
basic probability, basic statistics, Brownian motiion
Program
Random measures and Poisson random measures
Semimartingales with jumps and Lévy processes
Semimartingale models for financial asset prices:
Brownian SM, finite activity jumps,
infinite activity jumps, pure jump models
Quadratic variation
Estimating the jumps given discrete observations
Testing for jumps
Bibliography
Didactic methods
Classroom lessons, assignments consisting in the study of the proof of some results then to be told and commented on in class
Learning assessment procedures
Each student can choose either a written exam about one of the topics dealt with during the course, or an individual written and reasoned report deepening one of the topics of the course
Assessment
Rigor, creativity, exposure
Criteria for the composition of the final grade
Rigor 4 points out of 10, creativity 3, exposure 3
Scheduled Lessons
| When | Classroom | Teacher | topics |
|---|---|---|---|
|
Tuesday 29 October 2024 15:00 - 17:30 Duration: 3:00 AM |
To be defined | Cecilia Mancini | Stochastic models for financial asset prices: Brownian semimartingales. Motivations for introducing jump components: 1.visual inspection at specific time resolutions; 2. log-returns heavy tails; 3. short term option prices. Aims of a model: 1. measuring risk; 2. derivative pricing; 3. hedging the risk. Semimartingales with jumps. The simplest jump tool: the Poisson process (PP). Problems linked to the presence of jumps: testing for jumps, estimating the model coefficients. Outline of the course |
|
Tuesday 05 November 2024 15:00 - 17:30 Duration: 3:00 AM |
To be defined | Cecilia Mancini | Paths of Ito SMs with/without jumps, cadlag feature, jump activity index. The Poisson process: preliminaries, properties of finite values, piecewise constant paths, continuity at one point a.s., continuity in probability, probability of assuming a value n |
|
Thursday 14 November 2024 16:00 - 18:30 Duration: 3:00 AM |
To be defined | Cecilia Mancini | The Poisson process: cadlag paths, infinite divisibility, stationary and independent increments, Markov property. Lévy processes, counting processes, finite activity jumps, cadlag path and finitely many jumps above a threshold, infinite activity jumps and dense jump times. Compensated Poisson process, random measure associated to a PP, integrals with respect to a Radon measure |
|
Thursday 21 November 2024 16:00 - 17:40 Duration: 2:00 AM |
To be defined | Cecilia Mancini | Random jump measure associated with a stochastic process with cadlag paths, representation with Dirac deltas, examples: Poisson process jump measure, Compound Poisson process (CPP) jump measure. The compensator of the CPP, compensator of a Lévy process, Lévy measure and compensating measure. Finite/infinite jump activity characterized by the Lévy measure. Noticeable examples of integrals with respect to a jump measure, quadratic variation (QV) of a semimartingale as a crucial measure of the risk of a financial asset, examples: Brownian motion, CPP, and pure jump processes, Ito semimartingales. Importance of disentangling the Brownian risk from the jump risk, practical difficulty in disentangling given discrete observations |
|
Thursday 16 January 2025 15:00 - 17:30 Duration: 3:00 AM |
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] |
Cecilia Mancini
Amorino Chiara |
CTE
Stochastic processes: adapted, with finite/infinite variation paths, examples. Lévy processes: jump frequency, characterization of the paths properties through the Lévy measure, examples. Stopped process, semimartingales (SMs), paths representation, financial meaning of the components, compensator of the measure associated to the jumps of a SM, examples |
|
Tuesday 21 January 2025 15:00 - 17:30 Duration: 3:00 AM |
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] |
Cecilia Mancini
Chiara Amorino |
CTE
Semimartingales: integrals with respect to the compensated jump measure, examples, quadratic variation, characteristic triplet of a SM, Ito SMs, the special case of the Lévy processes, examples. Poisson and compensated Poisson random measures and their Lévy measure, Grigelionis representation of the paths of an Ito SM. |
|
Wednesday 22 January 2025 15:00 - 17:30 Duration: 3:00 AM |
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] |
Cecilia Mancini
Chiara Amorino |
CTE
Properties of the Brownian motion (BM) paths, properties of a stochastic integral with respect to a BM. Given discrete observations of an Ito SM, disentangling the jumps using Threshold Realized Variance. The asymptotic theory, examples of threshold choices. Bipower variation and its use to test for the presence of jumps. |
