Learning objectives
SKILLS TO BE DEVELOPED AND LEARNING OUTCOMES EXPECTED
1) Knowledge and understanding.The course aims to provide the basic
tools most suitable for the analysis of some fundamental aspects of
monetary and financial market. In module I, particular attention will be paid to time
series of financial issues: exchange rates, interest rates, prices and
equity returns, prices and yields of derivatives.
During the II module, the students will learn the basic concepts of probability theory, which are employed to construct and analyze models of financial markets under uncertainty.
The student will also learn the basic principles of arbitrage pricing and completeness in the market, notions which will be described and analyzed in detail in an elementary model but can be easily extended to more complicated frameworks. Finally, we will illustrate how to represent preferences for a rational decision maker and how to optimally select of a portfolio, given the returns and covariances of the traded assets.
2) Ability to apply knowledge and understanding . At the end of the
course, the student will be able to implement in an autonomous way the
techniques described above. The student will have therefore
developed specific skills, they are associated with critical skills for
diagnostic, which are essential ingredients in building a good statistical and probability
model, with the possible assistance of the appropriate level of computer
tools.
3) Making judgments .At the end of the course, the student will be able to
perform independently all the considerations regarding the problems of
analysis of financial time series correctly interpret the results of such analyses, even when made by other
users or experts. The student will also be able to construct probabilistic models for real life situation. In particular, the student will be able to construct an elementary model for a financial market under uncertainty, to analyze the properties of this market and compute in this framework prices of derivatives and portfolio strategies.
4) Communication skills . At the end of the course, the student will be
able to use appropriate technical language in communicating with the
operators of financial markets. Also he/she should be able to summarize the
statistical information of considerable size
5) Learning skills. We want to give the student the opportunity to
assimilate the key results of the statistical and probability theory that
form the basis of building a statistical model of a financial model under uncertainty. At the end of the course,
the student will have acquired the key concepts to be able to accurately
use quantitative tools, if they become necessary in the solution of
concrete problems of a financial nature.
Prerequisites
Knowledge of basic elements of calculus and financial mathematics, basic descriptive and inferential statistics
Course unit content
Elementary theory of stochastic processes for stationary series.
Empirical evidence of the observed time series.
Overview of analysis of the trend of stock market prices and moving averages.
Introduction to probability theory: the various approaches. The axiomatic approach. conditional probability and Bayes'theorem. Random numbers: the discrete case and the continuous case. Random vectors. Basic notions on financial markets. One-period financial market. Fundamental theorems of asset pricing. Pricing of derivatives. Introduction to expected utility theory. Portfolio selection: Markowitz's model.
Full programme
Elementary theory of stochastic processes for stationary series:
recalls elements of probability 'for random vectors;
transformation of univariate and multivariate random variables;
gaussian and White Noise processes; brief introduction to non-stationary processes of type Random Walk.
Empirical evidence of the observed time series:
empirical characteristics of the time series of financial returns and
formulas combinations of multi-period returns;
the shape of the distribution of returns; test of symmetry, kurtosis,
and normality; the time dependence (linear and nonlinear) of returns; autocorrelation function and tests of significance 'associates; autoregressive processes for stationary series of returns and
transforms associated with them.
Overview of analysis of the trend of stock market prices and moving averages.
Introduction to probability theory. Classical, empirical and subjective approaches. Axiomatic approach: sample space, sigma-algebra and probability measure. Axioms of probability. conditional probability, Bayes theorem. Random numbers, measurability. Distribution function. Discrete random numbers: probability mass function. Continuous random numbers: density function.
Expectation, variance and standard deviation. Moments of a random number.
Random vectors. Independent random numbers. Covariance and correlation.
Introduction to financial market. A 1-period financial market, with zero e non-zero interest rate.
Law of one price. Arbitrage and completeness. State price densities and risk-neutral probabilities. Fundamental theorems of asset pricing. Derivatives: call and put options. Put-call parity. Forward contracts and forward prices.
Introduction to expected utiltiy theory. Von-Neumann-Morgenstern axioms. Expected utility theorem. Portfolio selection: mean-variance principle. Markowitz's model.
Bibliography
GOZZI G., Strumenti Statistici per l’Analisi dei Mercati Finanziari, Libreria
Medico Scientifica , Parma, Edizione 2018 e materiale didattico
integrativo
caricato sul portale Elly del Dipartimento di Scienze Economiche e
aziendali (http://sea.unipr.it/it).
Libri di approfondimento:
Alexander, C. (2008), Quantitative Methods in Finance, John Wiley & Sons
Ltd,
C h i c h e s t e r , E n g l a n d . http://npu.edu.ua/!ebook/book/djvu/A/iif_kgpm_Carol_Quantitative_Methods_in_Finance.pdf.pd
f
De Luca , G. (2013), Metodi statistici per le decisioni nanziarie, Università
Parthenope a.a. , 2011-2012, Napoli
http://www.economia.uniparthenope.it/modifica_docente/deluca/msdf.pdf
Gallo G.M. e Pacini B. (2002), Metodi quantitativi per i mercati finanziari,
Carocci
Editore, Roma.
Di Fonzo T. e Lisi F. (2005), Serie storiche economiche. Analisi statistiche
e
applicazioni, Carocci editore, Roma
Laurini F. (2012) Elementi di analisi delle serie storiche finanziarie,
Libreria Medico
Scientifica , Parma
Pelagatti M.M. (2009), Statistica dei Mercati Monetari e Finanziari ,
Università
Milano - Bicocca.
http://www.statistica.unimib.it/utenti/p_matteo/lessons/SMMF/StatFin.pdf
Proietti T. , Econometria Applicata, Dipartimento di Scienze Statistiche,
Università
d i U d i n e .
http://www.statistica.unimib.it/utenti/p_matteo/lessons/SSE/EcAppl_Dispe
nse.pdf
Ruppert D. (2003), Statistics and Finance . An introduction, Springer, New
York
Tsay, R.S. (2010), Analysis of Financial Time Series, Third Edition,Wiley,
New York
E. CASTAGNOLI, Brevissimo Abbecedario di Matematica Finanziaria, scaricabile dalla pagina Elly del corso, o disponibile presso il Centro fotocopie del Dipartimento.
E. CASTAGNOLI, M. CIGOLA, L. PECCATI, Probability. A Brief Introduction, Egea, 2009.
S. PLISKA, Introduction to Mathematical Finance: Discrete Time Models,
Blackwell,
Malden 1997 (Seconda edizione).
T. BJORK, Arbitrage Theory in Continuous Time, Oxford University Press,
Oxford 1999.
Teaching methods
Acquisition of knowledge: a theoretical (oral) exposition of the several topics will be given, supported by a detailed discussion of examples and exercises.During Module 1, it will be used the software Microsoft Excel e di Gretl.
Acquisition of the ability to apply knowledge: tutorials and exercise sessions.
Acquisition of judgements: the students will be asked to choose the right instrument to solve a problem and to discuss strenghts and weaknesses of the several tools.
Acquisition of learing skills: for each topic, several problems will be shown and a critical analysis of the possibile solution will be carried on.
Acquisition of technical language: technical terms will be explained and used during the course.
In the exercise sessions there will be a wide discussion of
examples and exercises, with particular attention to those of a more
financial nature. The participation of the students will be requested in the
resolution of these exercises
Exercises and tests from the previous years will be uploaded on the Elly platform at the beginning of the year. To download the material, registration to the online
course is required
Assessment methods and criteria
The exam is in written form.
The student will be required to complete two test, one per module, consisting in exercises and theoretical question.
For module I: The summative evaluation of the learning will be done through a written
test evaluated on a 0-30 scale. During the test, the student is asked to: 1)
present the theoretical arguments learned during the course, by
answering three open questions (5pt each) to ascertain the capacity of
communicate with an appropriate technical language. 2) solve exercises,
structured in severel questions (15pt), in order to test learning ability, the
capacty of applying knowledge to real problems, and the independence
of judgment.
For modul II:The summative evaluation of the learning will be done through a written
test evaluated on a 0-32 scale.
During the test, the student is asked to: 1) solve a problem, structured in
4 questions, aimed at the analysis of an elementary model of
financial market (20pt) in order to test learning ability, the capactiy of
applying knowledge to real problems, and the independence of
judgment; 2) present the theoretical arguments learned during the
course, by answering two open questions (6pt each) to ascertain the
capacity of
communicate with an appropriate technical language.
The finale grade will be the average of the grades of the two tests. If the grade in one of the 2 test is below 10, the whole exam will be considered failed.
The “lode” is awarded if the highest score is reached in every exercise. and the student has shown a consideable knowledge of the topics presented in both modules.
A scientific calculator may be used during the test.
The text of the tests with their solutions will be uploaded to Elly within a week
after the test.
The result of the exam will be communicated to the students via Esse3 within 10 days.
The detailed results (the evaluation of each test) will be uploaded on the Elly platform.
Please note that online registration for the appeal is mandatory.
Other information
Elective assignment will be proposed to the students, to be possibly solved in group. The results will be taken into account in the final evaluation.
The bonus points obtained through the assignment will be valid for the all academic year.
