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


A.Y. Credits
2020/2021 8
Lecturer Email Office hours for students
Laura Gardini By appointment to schedule via email.
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

Assigned to the Degree Course

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

Learning Objectives

 The course aims to provide the basic elements of financial mathematics and classical valuation of bonds (items which have become indispensable in many of the sectors in which a graduate in Economics 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 are introduced, with examples and applications related to practices commonly ised 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.

6) Management elements of the bond portfolio: Market Coherence Hypothesis (or Absence of Arbitrage). Term structure, spot rates and forward rates. Extension of the structure by maturity and "coupon effect".

7) Duration and volatility of the value function. Its use in financial immunization techniques. Immunization techniques for flows with one and multiple outlets. Empirical methods in the use of immunization techniques.

Bridging Courses


Learning Achievements (Dublin Descriptors)

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

On the topics covered in the course, the financial sector, 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 during lessons and exercises.

Applying knowledge and understanding

The student must be able to apply the knowledge acquired, even under slightly different from the usual ones, 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. Examples of such applications are shown in the classroom during lessons and exercises

Communication skills

The student must be able to clearly communicate their claims and considerations of financial mathematics problems. The working mode is shown in the classroom during lessons and during exercises.

 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.

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


Frontal lessons.

Course books

Castagnoli, Cigola, Peccati, "Financial Calculus with applications" EGEA, Milano, 2013.

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


The exam consists of two written tests. A practical test consists of 3 exercises to be carried out in an hour. He was admitted to the theory test if you pass the practical test with a minimum score of 16/30. The theory test consists of answering five open questions, eg one on each of the five points listed in the program. The score script does mean, it's just an admission to the second part, which determines the rating, obtained by assessing from 0 to 6 points the answer to each of the 5 questions.

The exam consists of a written work, answering to five questions delivered by the teacher.

« back Last update: 01/04/2021


Questo contenuto ha risposto alla tua domanda?

Il tuo feedback è importante

Raccontaci la tua esperienza e aiutaci a migliorare questa pagina.

Se sei vittima di violenza o stalking chiama il 1522

Il 1522 è un servizio pubblico promosso dalla Presidenza del Consiglio dei Ministri – Dipartimento per le Pari Opportunità. Il numero, gratuito è attivo 24 h su 24, accoglie con operatrici specializzate le richieste di aiuto e sostegno delle vittime di violenza e stalking.

Posta elettronica certificata



Performance della pagina

Università degli Studi di Urbino Carlo Bo
Via Aurelio Saffi, 2 – 61029 Urbino PU – IT
Partita IVA 00448830414 – Codice Fiscale 82002850418
2021 © Tutti i diritti sono riservati