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
Second module, FIrst period:
Classes will take place online through the use of the Teams and Elly
platforms. They will be both synchronous (via Teams) and asynchronous
(uploaded on the Elly page of the course). Asynchronous lessons will be
dedicated to a rigourous exposition of the theory, for the acquisition of
knowledge.
Synchrounous classes will be mainly dedicated to the presentation of
examples and exercises. Students will be encouraged
to actively
participate to the discussion, to develop the ability to apply knowledge
and the acquisition of judgements and learning skills.
For the acquisition of technical language, the meaning of the specific
terms used in the course will be illustrated.
At the beginning of the course, one of the reference texts will be
uploaded to the Elly platform, as well as exercises and exam topics
assigned in previous years.
The teaching materials (slides) used during the lessons will also be
uploaded during the course.
To download the material it is necessary to register for the online course.
First module, Second period:
Classes will take place online through the use of the Teams and Elly
platforms. They will be both synchronous (via Teams) and asynchronous
(uploaded on the Elly page of the course). Asynchronous lessons will be
dedicated to a rigorous exposition of the theory, for the acquisition of
knowledge.
In the course of the lessons will be used to using Microsoft Excel and
Gretl. Gretl is an acronym for Gnu Regression, Econometrics and Time-
series Library. It is a software
package for econometrics that is easy to use and powerful enough. Gretl
is distributed as free software that can be downloaded from
http://gretl.sourceforge.net and installed on your personal computer.
Synchrounous classes will be mainly dedicated to the presentation of
examples and exercises. Students will be encouraged to actively
participate to the discussion, to develop the ability to apply knowledge
and the acquisition of judgements and learning skills.
For the acquisition of technical language, the meaning of the specific
terms used in the course will be illustrated.
At the beginning of the course, exercises and exam topics assigned in
previous years will be uploaded to the Elly platform.
Acquisition of knowledge: oral lessons. Acquisition of the ability to apply
knowledge: Tutorials
Acquisition of judgment: During the course students will be encouraged
to identify strengths and weaknesses of the statistical tools.
Acquisition of learning skills: for each topic will be provided an illustration
of the problem to solve and will analyze critically the solutions adopted.
Acquisition of technical language: while teaching you will learn the
meaning of terms commonly used in the analysis of financial time series.
The links to the videos will be available on Elly until December 31st, 2020.
Assessment methods and criteria
The summative evaluation of the learning will be done through a written
test: a quiz on Elly, with the use
of the Respondus software (alternativley, Teams will be used).
The instructions can be found on the web pages:
http://selma.unipr.it/;
http://selma.unipr.it/wp-content/uploads/Guida-Respondus.pdf;
https://elly2020.sea.unipr.it
The ID will be uploaded on a OneDrive foldere which link will be sent after
the deadline for the registration.
The test has a duration of 1 hour and consist of 22 multiple choice questions, each of which is
worth 3 points:
1st module 5 questions related to all the theoretical topics learned during the
course - (2) 6 questions each related to the result of solving a numerical
exercise on the topics addressed during the course.
2nd module: a problem, structured in 7 questions, aimed at the analysis of an
elementary model of financial market in order to test learning ability, the capacity of
applying knowledge to real problems, and the independence of
judgment; 2 theoretical questions on the theory of financial markets and
2 theoretical questions on probability theory to ascertain the capacity of
communicate with an appropriate technical language.
The exam is passed if at least 3 questions in each part are correctly answered and the final grade divided by 2 is at least 18. The "lode" will be attributed to a final grade strictly greater than 60.
The final test can alternatively be taken through two in itinere tests (module II at the end of the first period and module I at the end of the second), lasting 40 minutes each, structured for each module as described above. The test is passed if the evaluation in each intermediate test is at least 15 and the average is greater than or equal to 18.
In case of return to activity in presence, the summative evaluation of the
learning will be done through a written
test consisting in two parts, one for each module and each of one evaluated on a 0-33 scale.
FIrst module:he student is asked to:
1) explain the theoretical topics learned during the course, by answering
three open questions (6pt each) to ascertain the ability to communicate
with technical language. 2) solve exercises structured in several
questions (15pt), in order to test learning ability, the capacity of applying
knowledge to real problems and the judgment.
Second module: the student is asked to: 1) solve a problem, structured in
4 questions, aimed at the analysis of an elementary model of
financial market (21pt) in order to test learning ability, the capacty 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.
Simulation of the test in both forms can be found on Elly.
A scientific calculator and a copy of the TOOLBOX FOR THE WRITTEN EXAM may be used during the test. The TOOLBOX will be uploaded to Elly.
The text of the test with its solution will be uploaded to Elly within a week
after the test.
The result of the test will be published on Elly within 10 days after the
test.
Please note that online registration for the exam is mandatory.
Other information
Elective assignment will be proposed to the students during the First Period. The assignment will consist in 5 exercise on probabilty theory, which solution must be handed in before the end of the period and willl be evaluated on a 0-30 scale.
The students who deliver the solution of the exercises before the first
exam are exempt from answering to the probability questions (and attributed the grade of the assignment divided by 5 to these question).
