FINANCIAL MATHEMATICS (SEM)
Learning outcomes of the course unit
Knowledge and understanding
The student learns the main features of the basic quantitative models and methods for the valuation of:
- financial securities and credit instruments;
- future cash flows (originated by financial securities, economic investments, entreprises, and so on);
- structure of returns and prices of fixed-income securities.
The course deals with deterministic models only. Some discussion about models dealing with investments bearing financial risks is developed, with particular regard to financial immunization with respect to interest rate risk.
At the end of the course, the student should be able to perform the basic quantitative assessment of financial securities and credit instruments, to compare prices of fixed-income securities and to describe a problem of choice based on financial criteria.
Applying knowledge and understanding
The student will be trained in performing the basic quantitative assessments of financial securities and credit instruments, comparing market prices of fixed-income securities, setting a financial valuation problem or taking a decision based on financial criteria.
The course aims at developing the financial sensibility and the ability for critical analysis which are expected from a student graduated in the economic area, and who is employed in the financial sector, or deals with the financial management of commercial or industrial entreprises.
The student is educated in the use of the basic financial-quantitative language. He/she is able to interpret (and, if necessary, validate by autonomously developing appropriate calculations) the output of basic financial packages, as well as to describe them to third parties (such as users of financial services). Moreover, he/she is able to understand and describe the basic quantitative financial valuation criteria, commonly used for financial decision-making.
The student develops the ability to understand the financial problems and to select the most appropriate quantitative valuation models. The student learns to adopt deterministic quantitative models, also in a stochastic framework. In this latter respect, he/she understands which simplifications must be assumed in order to obtain a quick solution and how to interpret the main findings in respect of such simplifications.
Although not compulsory, a basic knowledge of the contents of Calculus is recommended.
Course contents summary
- Financial accrual, present value. The valuation of annuities. Mortgages.
- Net Present Value, Internal Rate of Return. Net Present Value and Economic Value Added.
- Price and yield to maturity of bonds. The term structure of interest rates (spot rates and forward rates). The non-arbitrage valuation principle.
- Interest rate risk. Immunization.
Available online, on the Elly platform. During the teaching period, the detailed program will be updated in the case of modifications.
- Samuel A. Broverman, Matematica Finanziaria. Edizione italiana a cura di A. Olivieri e G. Favero, Egea, Milano 2019.
- Course slides, available online the Elly platform, or in printed version at the copy centre of the Department of Economics and Management.
Face-to-face Lectures. During classes the theoretical features of models will be described, and through exercises their application to practical problems will be discussed. The student will be assigned problems which she has to solve autonomously after classes, so to develop her own ability to use the models presented during classes.
The slides used during classes are available since the beginning of the course online on the Elly Platform or, in printed version, at the copy centre of the Department of Economics and Management.
Assessment methods and criteria
Written exam (1hr available time).
Knowledge and understanding will be assessed through the request of solving three numerical problems (maximum grade: 6 over 30 each) and answering to three short questions (maximum grade: 4 each). Honors ("lode") may be awarded to students who, besides obtaining full marks, showed a particular in-depth knowledge and a relevant overall vision of the subject, together with an excellent ability in applying the gained knowledge and a particular care in drafting her assignment.
Part of the numerical problems will be declined in an original way in respect of the problems solved during classes, so to assess the ability to apply knowledge and understanding.
Making judgements and knowledge will be assessed through the request of interpreting some of the numerical findings.
In performing numerical calculations, commenting the numerical findings and the answers to the short questions, the student will be required to show her communication skills while using an appropriate technical language.
During the exam, use of a pocket calculator is admitted. No other device is admitted. The exam is "closed-book": consultation of teaching materials is not allowed.
The exam can be taken by attending three partial assessments organized during the teaching period. The first and the second partial tests (15 minutes time) require only the solution of numerical problems: they are "open-book" tests, as the consultation of teaching materials (slides, textbook, own notes) is allowed. The third partial test (40 minutes) requires solving a numerical problem and answering three short questions: as well as for the general test, in this test it is possible to use a pocket calculator only, and no other devices or materials are allowed.
Grades are published in Esse3 within one week from the exam. Detailed information is available on the Elly platform.