Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
primo semestre (lauree) dal Sep 28, 2020 al Dec 23, 2020.
The course aims to provide the knowledge of the basic quantitative tools and the classical mathematical models for the analysis and evaluation of the main financial transactions, financing contracts, economic-financial investment projects, bonds and term structure of interest rates, interest rate risk and portfolio selection. At the end of the lessons, the student must be able to set up a financial evaluation problem in formally and economically correct terms, and be able to obtain the solution and interpret it. Therefore, the teaching aims to develop the capacity for autonomous reasoning in the analysis and interpretation of concrete problems of choice in the economic-financial field.
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.
|Basso A., Pianca P.
||Introduzione alla Matematica Finanziaria
|Castellani, De Felice, Moriconi
||Manuale di Finanza I.
|P. Bortot, U. Magnani, G. Olivieri, F. A. Rossi, M. Torrigiani
|E. Castagnoli, L. Peccati
||Matematica in azienda Vol. 1: calcolo finanziario con applicazioni
The methods of learning assessment consist of a written test and an oral test.
The oral test is:
- optional if the written grade is greater than or equal to 20/30,
- compulsory if the grade at the written test is between 16/30 and 19/30
The written assessment is considered unsuccessful if the grade obtained is less than 16/30.
It would 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.
During the COVID-19 health emergency the intermediate test can be cancelled and the written exam could be carried out in telematic mode through Quiz Moodle with Zoom session and the oral exam could be carried out through Zoom session.