Economics and Finance

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.

Having passed the general mathematics exam having the knowledge of the basic concepts of the study of function, derivatives and integrals

Libro di testo: P. De Angelis, R. De Marchis. M.Marino; A.Martire - Lezioni di Matematica Finanziaria - Giappichelli EDITORE

Frontal lesson with use of blackboard, transparencies and personal computer

Attendance is recommended for passing the exam but it is not mandatory

The written test consists of three exercises and a theoretical / practical question. The time for the written test is 60 minutes The oral exam focuses on the whole program

Frontal lesson with use of blackboard, transparencies and personal computer

The course aims to introduce students to the fundamental principles of financial mathematics, providing the theoretical and practical tools necessary for the analysis and evaluation of financial operations. Particular attention is devoted to the study of intertemporal financial laws, annuities, and amortization plans, as well as to the criteria for comparing and selecting among certain financial operations. The course also covers the basic concepts of the term structure of interest rates and introduces the principles of financial immunization, with the goal of fostering an integrated understanding of the main temporal and valuation dynamics in financial markets. The course is organized into the following teaching modules: PART 1: Introduction to financial operations.Financial situations and preference criteria; financial operations. Intertemporal financial laws: capitalization and discounting; simple interest regime; commercial discount regime; compound interest regime; interest rates; nominal interest rate; complementary notions on capitalization; capitalization laws as solutions to first-order differential equations; mixed capitalization and comparison of accumulated values. PART 2: Annuities and amortization. Classification of annuities; definition and computation of the principal value, present value, and accumulated value of an annuity. Specific cases: whole, fractional, temporary, perpetual, due, immediate, constant, and variable annuities. Related problems: determination of duration, payment, and interest rate. Amortization plans: fundamental quantities and relationships; types of amortization: uniform or Italian, progressive with constant installments or French, and with accumulation quotas or American. PART 3: Selection among certain financial operations. Net Present Value (NPV) and Internal Rate of Return (IRR) criteria. The term structure of interest rates: financial equivalence in the market, bonds, spot and forward contracts, measurement of the term structure. Principles of financial immunization: Duration and Convexity.

The course has no formal prerequisites. However, it is advisable that students possess a solid basic knowledge of mathematics, with particular reference to the understanding and manipulation of the main mathematical functions, as well as to the calculation of derivatives and definite integrals.

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

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.

The exam will be administered in written form and will include open-ended questions and exercises. Specifically, the written test will consist of three questions covering the main topics discussed during the course, typically one for each teaching module. For open-ended questions, students are expected to provide complete and well-structured answers, demonstrating their ability to contextualize the applied techniques and models. In the exercises, students must show all the mathematical steps leading to the final result and provide appropriate explanatory comments. Each question will include several sub-questions, designed according to Bloom’s taxonomy, to progressively assess the student’s understanding, application, and analytical skills. An oral examination may be required only upon the instructor’s specific request, in particular cases or for further assessment purposes.

- 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

The course is delivered through in-person lectures, complemented by guided discussions, practical exercises under the supervision of the instructor, and self-assessment activities carried out through group work, flipped classroom and peer review. Occasionally, seminars led by experts from the field may be organized, with the aim of deepening specific topics and fostering the connection between theoretical concepts and real-world applications.