FINANCIAL MATHEMATICS (SEM)
Learning outcomes of the course unit
Knowledge and understanding:
The aim of the course is to describe 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.
It will also be discussed how to use such models and methods.
The models dealt with are deterministic. Some discussion about models dealing with investments bearing financial risks is developed, with particular regard to 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 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 enterprises.
The student is educated in the use of the basic financial-quantitative language. 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, 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, 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.
Price and yield to maturity of bonds. The term structure of interest rates (spot rates and forward rates). The non-arbitrage valuation principle. Duration.
Net Present Value, Internal Rate of Return. Net Present Value and Economic Value Added.
Interest rate risk. Immunization.
Available online, on the course site.
M. D'Amico, E. Luciano, L. Peccati, Calcolo finanziario. Temi di base e temi moderni, Egea, Milano, 2011.
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.
Assessment methods and criteria
Knowledge and understanding will be assessed through the request of solving three numerical problems (maximum grade: 18 over 30) and
answering to three short questions (maximum grade: 12).
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 in respect of the use of an appropriate technical language.