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, enterprises, and so on);
- Structure of returns and prices of fixed-income securities.
He will learn how to use such models and methods.
The models dealt with are deterministic. The student also examines simple models dealing with investments bearing financial risks, with particular regard to financial immunization in respect of 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 is 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 enterprises.
The student is educated in the use of the basic financial-quantitative language. He/she is able to interpret (and, if necessary, validate by developing autonomously 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 how 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
- Future value, 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 fixed-interest bonds. The term structure of interest rates (spot rates and forward rates). The non-arbitrage valuation principle. Mean duration.
- Interest rate risk. Financial immunization.
Available online, on the Elly platform. During the teaching period, the detailed program will be updated weekly.
- In Italian: Samuel A. Broverman (2019). Matematica finanziaria. Edizione italiana a cura di A. Olivieri e G. Favero. Egea, Milano
- In English: Samuel A. Broverman (2017). Mathematics of Investment and Credit. ACTEX Learning.
- Course slides, available online on 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 he/she has to solve autonomously after classes, so to develop her own ability to use the models presented during classes.
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
Knowledge and understanding is assessed through the request of solving three numerical problems (maximum grade: 6 over 30 for each problem) and answering to three short questions (maximum grade: 4 for each question).
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 is 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 is required to show his/her communication skills in respect of the use of an appropriate technical language.
During the exam, use of a pocket calculator is admitted. No other device is admitted. The exam is closed book: the consultation of whatever teaching material is not admitted.
Honors will be awarded to those particularly deserving students who, in addition to having complied with the requisites necessary to obtain full marks, in the performance of the test have proved an appreciable systematic knowledge of the subject, an excellent ability to apply the gained knowledge to the specific problem submitted during the exam, a considerable autonomy of judgment, as well as a particular care in the formal drafting of the paper.
It is possible to take the exam with three partial tests, organized during the teaching period. The first and second partial tests require only the solution of numerical problems. These tests, which last 15 minutes, are open book: the consultation of teaching material (text, slides or other) is admitted. The third partial test, lasting 40 minutes, requires the solution of a numerical problem and answering to three short questions; during this test it is possible to use a pocket calculator only, while other devices or the consultation of any teaching material are not allowed. Detailed information are available on the Elly platform.
The final grade is published in Esse3 within 8 days after the exam.