STATISTICS MODELS APPLIED TO FINANCE
Learning outcomes of the course unit
a) Knowledge and understanding. The course extends and complements the quantitative skills imparted by the previous teachings. In particular, it provides expertise on the main statistical methods for the analysis of financial phenomena of various kinds and deepens the problems of parameter estimation and diagnostics for a statistical model selection. These techniques include: the logistic regression model for credit risk; Markov models for linear and non-linear financial time series and diagnostic graphics. Participation in educational activities, in conjunction with the exercises of kit, enhance the student's ability to develop, independently, that type of "statistic" that characterizes the nature of the Master of Science in Finance and Risk Management.
b) Applying knowledge and understanding At the end of the course, the student will be able able to implement on their own the advanced modeling techniques above. The student will have therefore developed specific skills advanced, they are associated with critical skills for diagnostic, which are essential ingredients in building a good statistical model, with the possible help of appropriate information systems.
c) making judgements. At the end of the course, the student will be able to perform independently all the considerations regarding the financial problems of various kinds. In addition, the student will be able to correctly interpret the results of such analyzes, even when made by other users or experts. By studying the contents of the course, the student matures, therefore, a high degree of autonomy aimed at the correct judgment of the application of proper technique and the associated ability to rework the quantitative knowledge acquired, in order to maximize the relevant information in the content start key risk managment.
d) communication skills. At the end of the course, the student will be able to interact constructively with the financial figures of each profile. The ability to summarize the statistical information of a complex nature, providing, in addition, effective quantitative synthesis, allows the student to contribute their thoughts to the development and drafting of the decision-making processes.
e) learning skills. We wish to give to the student the opportunity to assimilate the key results of the theory of mathematics, statistics and probability that underlie the construction of a statistical model. 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.
Course contents summary
The course presents the main statistical methods and analysis of financial data for the management of risk and expected thunderstorms:
a) The statistical model and the likelihood function: Parametric models for independent components, maximum likelihood estimators and asymptotic properties;
b) The logistic regression model for credit risk;
c) Linear models for time series, elements of Markov chains and ARMA processes for stationary series;
d) Non-Linear Models: Models ARCH (1) and GARCH (1,1) an outline to their generalizations.
The basic theory necessary to understand the use of methodologies and awareness for mastering with the results, will be accompanied by exercises in the classroom, with both probabilistic and computational features using Excel, R and GRETL.
1) Main reference
Notes covering all contents (in preparation).
2) Preliminary reference for students with minor gaps
Laurini, F. (2012) "Elementi di Analisi delle Serie Storiche Finanziarie". Libreria Medico Scientifica. (Italian)
3) Further references
a) Azzalini, A. (2001) "Inferenza Statistica: Un'introduzione Basata Sul Concetto Di Verosimiglianza". Unitext / Collana Di Statistica E Probabilità Applicata. Springer, seconda edizione. (Italian)
b) Harvey, A.C. (1993) "Time series models". Cambridge, MA: MIT Press, seconda edizione. (English)
c) Tsay, R.S. (2010) "Analysis of Financial Time Series". Wiley-Interscience, terza edizione. (English)
The knowledge and understanding will be assessed with 1 open-ended question with a short exercise on some important points of the theory of the value of 8/30
The ability to apply knowledge will be assessed with 2 exercises worth 11 points each.
Judgement ability to learn will be assessed through the drafting of relevant comments regarding the 2 exercises above.
The ability to communicate with technical language will be assessed by the appropriate links between different points of the program in the event of an oral supplementation of the test.
Assessment methods and criteria
Written exam with oral supplementation optional.