FINANCIAL MATHEMATICS

Course objectives

The primary learning outcome of this subject is to allow students to learn theoretical elements and basic mathematical instruments to evaluate elementary financial operations. Furthermore, students must know how to interpret the results of their application to real problems. Specific objectives Knowledge and understanding: After attending the course, students know and understand the problems related to the evaluation of the basic financial operations and mathematical models to be used to solve such problems. Capacity to apply knowledge and understanding: At the end of the course, students can formalize basic financial operations, according to the correct mathematical approach and apply specific models of the subject, to solve evaluation problems. Autonomous judgment: At the end of the course, students can collect and read data concerning basic and complex financial, borrowing-and-lending as well as investment operations, also in a context governed by fixed or varying interest rates. Communication skills: At the end of the course, students can explain and represent problems and solutions in the financial field, through the methods acquired. Learning skills: At the end of the course, students acquired basic financial logic that will allow them to approach further studies in the area of theories and processes of complex financial markets.

Channel 1
ROBERTO DE MARCHIS Lecturers' profile

Program - Frequency - Exams

Course program
Financial transactions. The capital market. The structure of prices and interest rates in the capital market. Laws and financial regimes. Equivalent rates. nominal rates. Yield to maturity. made financial transactions. present value of an annuity and upright. Classification of an annuity. current and uprights in different financial regimes values. Problems with constant annuities: the present value search, the installment, the number of installments, the interest rate. temporal indices and variability. Establishment of a capital. general transaction scheme. Typical problems in capital formation. Amortization of loans. The elementary and the financial setting. Depreciation methods. Usufruct and bare ownership. Evaluation and selection of financial projects. R.E.A. criterion, the T.I.R. and T.R.M. Term structure of interest rates, financial immunization principles.
Prerequisites
Having passed the general mathematics exam having the knowledge of the basic concepts of the study of function, derivatives and integrals
Books
Libro di testo: P. De Angelis, R. De Marchis. M.Marino; A.Martire - Lezioni di Matematica Finanziaria - Giappichelli EDITORE
Teaching mode
Frontal lesson with use of blackboard, transparencies and personal computer
Frequency
Attendance is recommended for passing the exam but it is not mandatory
Exam mode
The written test consists of three exercises and a theoretical / practical question. The time for the written test is 75 minutes The oral exam focuses on the whole program
Lesson mode
Frontal lesson with use of blackboard, transparencies and personal computer
Channel 2
VALERIA D'AMATO Lecturers' profile

Program - Frequency - Exams

Course program
1. Capitalization and discount Capitalization Discount Equivalence of interest rates Simultaneous capitals Decomposability. Cantelli Theorem 2. Annuities certain Integer and constant annuities Annuities in arithmetic acceleration Annuities in geometric acceleration Fractional annuities 3. Amortized loans Description The different modalities of loan’s reimbursement 4. Bonds loans The mathematical description The different modalities of a bonds loan’s reimbursement. Yields associates with a bonds’ loan Basic model for the determination of a bond value 5. Investment analysis The different criteria for investment analysis The analysis of a single investment The choice among several investments Fixed income bonds. Interest Rate Term Structure. Duration: financial immunization and volatility of the bond price.
Prerequisites
Foundation of mathematics. Study of function
Exam mode
Written and oral tests
Lesson mode
Lessons in presence
IMMACOLATA OLIVA Lecturers' profile

Program - Frequency - Exams

Course program
The syllabus for the first part of the course (3 CFU) is defined as follows: o Introduction to financial transactions. Financial situations and preference criteria, financial transactions. o Inter-temporal financial laws. Capitalisation and discounting, Simple interest regime, Commercial discount regime, Compound interest regime, Interest rates, Nominal interest rate, Complementary notions on capitalisation, Capitalisation laws as solutions of first-order differential equations, Mixed capitalisation and comparison of mounds. o Annuities. Value of a financial transaction in a compound regime, Generalities on annuities, Fundamental formulas of geometric series, Present value and uppercase of an annuity, Case of fractional annuities, Case of perpetual annuities, Problems related to annuities, Determining the duration, Determining the installment, Determining the rate.
Prerequisites
There are no compulsory prerequisites for the course, but it is crucial that students have a basic knowledge of mathematics. Therefore, it is required that students have passed the basic mathematics course exam and are able to manipulate mathematical functions, derivatives and integrals.
Books
Reference book: P. De Angelis, R. De Marchis, M. Marino, A.L. Martire (2023) Lezioni di Matematica Finanziaria, Geppichelli Editore. Further books (not mandatory): M. Frezza (2019) Esercizi di Matematica Finanziaria. Svolti e commentati, McGraw-Hill Education G. Castellani, M. De Felice, F. Moriconi (2005) Manuale di Finanza. I Tassi d'interesse. Mutui e obbligazioni, Il Mulino
Frequency
The lectures are delivered in person: the lecturer teaches in the Faculty classrooms, using the IT equipment available, and students are required to attend in person. Teaching materials are made available to students in a dedicated Classroom.
Exam mode
The assessment procedure is based on a written test with open-ended questions and\or exercises. In particular, the exam will consist of three questions related to some topics covered during the lectures. In case of open-ended questions, students will be required to provide an exhaustive answer, attempting to contextualize both the techniques and the modelling used. As for the exercises, students are required to show the whole mathematical procedure that leads to the final result, also providing appropriate comments.
Bibliography
- G. Castellani, M. De Felice, F. Moriconi (2005) Manuale di Finanza. I Tassi d'interesse. Mutui e obbligazioni, Il Mulino - P. De Angelis, R. De Marchis, M. Marino, A.L. Martire (2023) Lezioni di Matematica Finanziaria, Geppichelli Editore. - M. Frezza (2019) Esercizi di Matematica Finanziaria. Svolti e commentati, McGraw-Hill Education
Lesson mode
The course is based on standard classroom lectures
  • Lesson code1017164
  • Academic year2024/2025
  • CourseEconomics and Finance
  • CurriculumEconomia e finanza
  • Year3rd year
  • Semester1st semester
  • SSDSECS-S/06
  • CFU9
  • Subject areaAttività formative affini o integrative