Student guide Facoltą di Economia A.A. 2005/06 Lauree Triennali

Financial Mathematics
Aim of the course
The course deals with some mathematical tools (models and procedures) which support financial decisions. These tools can be used to value, compare, design financial contracts as well as hedge them against a risk. While presenting the different tools, the course attempts to develop the students' ability to recognise the essential aspects of a financial problem in order to formalise them using a mathematical model. There are two aims - to familiarise the students with financial calculation and to develop their ability to represent reality by using models.
Emphasis is placed on models and procedures which can be used in practice. The material covered in each unit progresses from the simplest concept to the more advanced one.
First the fundamentals of financial calculus are presented as well as its basic applications. The acquired notions are then used to examine such problems as the selection of investment and/or finance projects, the estimation of a term structure of interest rates, the management of interest rate risk, the selection of a portfolio.
1. Financial calculus.
Financial principles: accumulation and discount of money (simple and compound interest; simple, compound and trade discount). Forces of interest and discount. Annuities and perpetuities. Investment plans. Amortisation of a debt. Instalment loans.
2. Financial decisions.
Selection of investment and/or finance projects: net present value and internal rate of return criteria. Comparative analysis of such criteria. Computation of the internal rate of return.
3. Fixed income securities and term structure of interest rates
Valuation of pure discount and coupon bonds. Duration and variability of a bond price. Spot and forward rates. Estimation of a term structure of interest rates.
4. Portfolio management.
Immunization against interest rate risk. Portfolio selection: mean-variance framework, representation and derivation of efficient portfolios, risk diversification, separation theorem.
Attenders will take a written exam at the end of the course. The exam for the remaining students is oral.
Reading list
Castagnoli, E., Peccati, L., Financial calculus with applications, Le dispense del pellicano - Egea, 2002.
Luenberger, D.G., Investment Science, New York, Oxford University Press, 1998.
Additional references may be made available in class.