Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
primo semestre (lauree) dal Sep 20, 2021 al Jan 14, 2022.
The objectives of the course are the introduction of the pillars of financial contracts and the quantitative method for their management, to be developed to the foundations of fixed income and portfolio management. The course will introduce the basic jargon in finance, as well as the main concepts underlying asset valuation and assessment of risk. At the same time, the course will develop quantitative methods which will be useful for advanced courses in finance. At the end of the course, the student is expected to be able to perform operations involving the financial instruments explained in class, and to understand the theoretical ideas illustrated in the course. Basic knowledge of mathematics and statistics is strongly recommended.
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.
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.
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.