Università degli Studi di Urbino Carlo Bo / Portale Web di Ateneo


A.Y. Credits
2016/2017 6
Lecturer Email Office hours for students
Laura Gardini

Assigned to the Degree Course

Economics and management (L-18)
Date Time Classroom / Location

Learning Objectives

The course aims to provide the basic elements of financial mathematics and classical valuation of bonds (items which are necessary in many of the sectors in which a graduate in Economics and Management may operate), and aims to teach to perform the most common financial calculations (valuation of flows, amortization schedules, bonds, spot and forward interest rate structures). To this end, the basic concepts of standard financial mathematics era introduced, with examples and applications related to practices commonly used in workplaces and in financial markets.


1) Common financial laws: financial laws depending on one variable and financial laws depending on two variables. Simple interest accumulation process, Simple discount (or Rational Discount), Linear (bank) discount, Compound Accumulation Process (or Exponential Accumulation Process) and Compaund discount (exponential rule). Comparison between financial laws described with different formulas. Average interest intensity. Instantaneous interest intensity or instantaneous interest rate or force of interest. Decomposablility. Spot rates and forward rates.

2) Certain annuities and Constitution of Equity. Simplifying the computations for annuities. Annuities Values with constant installments. Annual annuity / perpetual unitary, delayed / advance, immediate / deferred annuities. Establishment of a capital with constant installments / advance, immediate / deferred. Annuities with variable rates.

3) Amortization (redemption) of a loan: Generalities. Gradual amortization, Elementary Closure (or Settlement) Condition, Initial Closure (or Settlement) Condition, Final Closure (or Settlement) Condition. The most popular amortization plans. Amortization with constant capital shares, amortization quotas (Italian amortization). Amortization with constant installments (French amortization). Financial leasing.

4) Financial choiches and financial objective. Evaluation of financial flows: Net present value (NPV) Internal (or Implicit) Rate of Return (IRR). The TRMmodel. Comparison between NPV and IRR. Financial leverage, Return on Equity (ROE). Arithmetic Average Maturity (Average Term to Maturity). Financial Average Maturity. Financial Duration. Flat Yield Curve Duration. Modified Duration and Convexity.  Volatility estimation.

5) Bonds and fixed income coupon bonds. Treasury bills (BOT). Bullet bonds (BTP). Evaluation of bonds.

Bridging Courses


Learning Achievements (Dublin Descriptors)

Learning outcomes and competences to be acquired

It is expected the learning of the basic elements of classical mathematical finance leading to the knowledge and understanding of this subject and to its use and application  in the framework of different contexts.

The ability of the autonomous use of the financial techniques in several activities and works in this sector are also expected, as well as making  autonomous judgements ability, learning and communication abilities.

Knowledge and understanding

The student must acquire the basic knowledge for understanding the key financial variables and their use in the calculation models. Examples and working mode are shown in the classroom.

Applying knowledge and understanding

The student must be able to apply the knowledge acquired, even under slightly different assumptions, and to understand and solve realistic problems of financial mathematics. Examples are shown in the classroom during lessons and exercises.

Making judgements

The student must have the ability to use the acquired knowledge to solve problems by themselves that may appear new.

Communication skills

The student must be able to clearly communicate their claims and considerations of financial mathematics problems.


Learning skills

The student must have learned the material so that they can undertake further study paths also independently having acquired the skills needed to develop new knowledge and professional skills. Examples will be given in the classroom.

The verification of learning takes place through talks in the classroom and at the examination.

Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Didactics, Attendance, Course Books and Assessment

Course books

Chapter 1,2,3,4,5 from “R.L. D’ecclesia e L. Gardini, Appunti di matematica finanziaria. Giappichelli, Last Edition.


The exam consists of two written tests. A practical test consisting of 3 exercises to be carried out in an hour. A student is allowed to the theory test if the practical test is passed with a minimum score of 16/30. The theory test consists of five open questions, one on each of the five points listed in the program. The rating is determined only by the theory test, obtained by assessing from 0 to 6 points to each of the 5 questions.

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