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Oggetto:
Oggetto:

FINANCE & INVESTMENTS

Oggetto:

FINANCE & INVESTMENTS

Oggetto:

Anno accademico 2021/2022

Codice dell'attività didattica
SEM0107
Docenti
Paolo Ghirardato (Titolare del corso)
Stefano Baccarin (Titolare del corso)
Corso di studi
ECONOMIA - percorso in Economia e Data Science
ECONOMIA - percorso in Economia e Finanza
ECONOMIA - percorso in Economia e Management
ECONOMIA - percorso in Scienze Economiche
Anno
3° anno
Periodo didattico
Primo semestre
Tipologia
Affine o integrativo
Crediti/Valenza
6
SSD dell'attività didattica
SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz.
Modalità di erogazione
Tradizionale
Lingua di insegnamento
Inglese
Modalità di frequenza
Facoltativa
Tipologia d'esame
Scritto
Prerequisiti
A good knowledge and understanding of basic Calculus for Economics and Finance (at the level of the course of Matematica per l'Economia I) and of Optimization, Financial Mathematics and Linear Algebra (at the level of the course of Matematica per l'Economia II).
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Sommario insegnamento

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Obiettivi formativi

This is a course which introduces students to the basic ideas of Mathematical Finance. While the course's emphasis is on theoretical issues, specific attention is given to the application of the concepts developed in class for designing successful investment strategies. 

 


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Risultati dell'apprendimento attesi

At the end of the course, the student is expected to be capable of:

-using the basic tools and results to pose, formalize and analyse an investment decision problem,

-understanding the methods used in the investment industry to allocate assets and construct efficient portfolios

-knowing the extent to which the results presented in the course are dependent on the assumptions that are made about the market environment, and therefore the extent to which such results are robust 

-being able to communicate such findings using appropriate and clear mathematical notation and language


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Modalità di insegnamento

 

The course-work is articulated in 48 hours of formal lecture time, and in at least as many hours of at-home work solving practical exercises.

The course will be taught in-person, but classes will also be streamed via Webex, so that students who cannot participate in-person may still be able to attend and participate. The course schedule (with venues) is the following:

  • TUESDAYS 11:15-13:15, Aula Magna (Nuovo Polo Didattico)
  • FRIDAYS 14:00-17:00, Aula 5
Students who want to participate in-person will need to sign up using the "student booking" app (recall that access to the School's building requires a valid "green pass"). Students who are attending classes remotely can log in using the link provided below. Attendance in-person is strongly recommended.
 
 


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Modalità di verifica dell'apprendimento

The course grade is determined solely on the basis of written examinations.  The objective of the examination is to test the student's ability to do the following:

1) Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results.

2) Use effectively the concepts and the results to solve simple investment choice problems.

Practicalities:

There are 6 possible exam sessions in each academic year. The first session takes place at the end of the first semester (before the winter break), while the remaining five sessions are held from January to September. The details for the examination are provided below.

Each exam lasts 120 minutes, and it is typically articulated in 6 questions. Some of the questions have an essay part, and some of the questions also have a more practical ("exercise") part. Each question is scored around 10 points, and the maximum score for the exam is 60. The final score in 60ths is computed, and it is transformed into 30ths, taking also into account the general class performance (i.e, giving some weight to relative, as well as absolute performance).


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Attività di supporto

Office hours will be announced soon on the course's Moodle page.

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Programma

The course offers a quick presentation of some of the fundamental ideas of modern Mathematical Finance. It is divided in three main sections (topics in parentheses will be covered only if time allows).

Section 1 (Ghirardato): Arbitrage Pricing Theory

  • The one-period model, with and without interest 
  • Derivative securities; complete and incomplete markets
  • More than one period: conditional prices and the Binomial Model
  • Sublinear prices
  • (Options)

Section 2 (Ghirardato): Choice under uncertainty

  • Basic ideas
  • Stochastic dominance
  • The Expected Utility Model, risk aversion and utilities
  • (Paradoxes)

Section 3 (Baccarin): The Markowitz portfolio selection model

  • The portfolio problem: general setup, with and without a risk-free security
  • The Mean-Variance tradeoff problem and efficient diversification
  • An introduction to the Capital-Asset Pricing Model

 


Testi consigliati e bibliografia

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The exam is going to be based on the class notes. The recommended textbook (which follows closely the class syllabus) is in Italian, but English texts that cover the course material are suggested below.

For the sections on Arbitrage Pricing and Expected Utility:

  1. Principles of Financial Economics, by S. LeRoy and J. Werner, Cambridge University Press 2001 (Chapters 1-10)

For the section on Portfolio Selection:

  1. Essentials of Investments, by Z. Bodie, A. Kane, A. Marcus, McGraw-Hill (chapters 5-6-7) 
  2. Corporate Finance, Global Edition, by J.Berk, P. DeMarzo, Pearson (chapters 10-11)


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Note

Links to the Webex sessions for the lectures are posted on the course's Moodle page.

 

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