Financial mathematics (2015/2016)

Course partially running (all years except the first)

Course code
Name of lecturers
Bruno Giacomello, Elisa Pagani
Bruno Giacomello
Number of ECTS credits allocated
Academic sector
Language of instruction
primo semestre dal Sep 14, 2015 al Jan 8, 2016.

Lesson timetable

Learning outcomes

The course introduces the basic quantitative tools for the analysis and evaluation of key financial transactions, contracts and financing of investment projects. They will also be addressed models for the introduction and discussion of the financial decisions in uncertain environment and in the presence of constraints.

While there will be no formal prerequisites to make profitable learning, it may also have already passed the examinations in Mathematics of the first year and Statistics of the second year.

The course consists of 72 hours of lectures and tutorials. There are also the hours of tutoring.


1. Read and financial regimes
Financial transactions: capitalization and discounting. Financial laws: upright, present value, interest, discount, interest rate and discount rate. Regime of simple interest, capitalization several times a year, compound interest, the discount trade. Equivalence between different laws and between interest rates of different periods. Force of interest. Financial arbitrage, severability of financial laws, spot rate, forward rates. Currency transactions. Nominal interest rates, inflation, real interest rates.
2. Financial transactions made
Financial transactions made and their classification. Current value and upright of a set of financial movements. Net present value (VAN or NPV). Evaluation of the installment, the number of installments, the implicit rate (TIR or IRR). Consumer credit, TAN and TAEG. Amortization schedules and closing conditions. Straight-capital basis, in equal installments on a straight interest paid in advance, with shares of accumulation. The pre-amortization. Early repayment of a mortgage. Rate mortgages indexed. Financial leasing. Savings plans.
Bonds and assessment of the price of a bond, estimates of the term structure of interest rates. Control / hedging of interest rate risk: duration and convexity.
Criteria for choosing between operations / financial projects: NPV, IRR, TRM, WACC.
3. Portfolio selection with two risky assets
Reminders of probability: the expected value, variance, correlation. Investment in assets yielding haphazard. Expected return and volatility / risk of a portfolio of assets. Risk aversion and Markowitz's model. Return and risk of a portfolio: an activity to yield randomly and one in certain return, two activities to yield uncertain, two activities to yield randomly and one in certain return. Capital Allocation Line. Capital Market Line.
4. Portfolio selection with n risky assets
Recalls matrix calculation. Correlation matrices and the covariance. Choices in the presence of constraints: the methods of Lagrange and Kuhn-Tucker. Markowitz's model with n risky assets. The conditions of the first order. The presence of activity in certain return. The separation theorem. The Capital Asset Pricing Model (CAPM). Eigenvalues and eigenvectors of a matrix. Principal Component Analysis (PCA).

Libri di testo
Notes and teaching material available online through the page e-learning course.
E. CASTAGNOLI, L. PECCATI, Matematica in azienda 1: calcolo finanziario con applicazioni, EGEA Bocconi, Quarta Edizione Milano 2010.
A. BASSO, P. PIANCA, Introduzione alla Matematica Finanziaria, Cedam, Padova, 2010.
P. BORTOT, U. MAGNANI, G. OLIVIERI, F.A. ROSSI, M. TORRIGIANI, Matematica finanziaria, seconda edizione con esercizi, Monduzzi, Bologna, 1998.

Assessment methods and criteria

It 'will be a final examination intermediate.
The intermediate test is introduced in order to stimulate students to the systematic study and regular matter during the course, in order to improve the learning process in view of the close functionality, the methods and models from time to time discussed with subsequent arguments.
Such evidence shall be in writing and shall cover the program topics addressed until then.

The intermediate test is optional, and if successful allows to gain a bonus, which will be added to the mark achieved in the final written test, valid only for the exams that conduct at its next meeting in lessons, as follows :
- 1 bonus point if the vote of the intermediate test is between 18 and 23;
- 2 bonus points if the vote of the intermediate test is between 24 and 26;
- 3 bonus points if the vote of the intermediate test is between 27 and 30.

In any case for passing the exam is a written test final on all matters scheduled and divided into several questions inspired by the examples presented in the classroom as well as to those contained in the available on-line material, aimed at ascertaining:
- Knowledge of the topics scheduled
- The ability to apply methods and models to various economic and financial issues.
The Commission may request an oral evaluation in order to verify:
- The depth and breadth of knowledge acquired;
- The properties of language, the mastery of knowledge and presentation skills;
- The ability to connect to the systemic form of the knowledge acquired.