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


A.Y. Credits
2020/2021 8
Lecturer Email Office hours for students
Fabio Tramontana By appointment. Contact the teacher through email

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 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.

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)

Learning outcomes and competences to be acquired

At the end of the course the student must have gained a good command of the financial mathematics topics discussed in the course. He/she will have to be able to properly carry out the studied cash flow computations, and be able to understand the appropriateness of the main financial variables and processes. Working examples are shown in the classroom during lessons and exercises.

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 computation models. Examples and working mode are shown in the classroom during lessons and exercises.

Applying knowledge and understanding

At the end of the course the student must have acquired a good ability to use financial variables studied in situations similar to those presented in the course. He/she should be able to properly apply the studied formulation and be able to solve financial mathematical problems similar to those studied. In particular, he/she must be able to apply acquired knowledge even in contexts slightly different from those studied and have the ability to use the acquired knowledge to solve problems that may appear new. Examples of such applications are shown in the classroom during lessons and exercises.

Making judgements

At the end of the course, the student must have acquired a good ability to analyze subjects and problems of financial mathematics, the ability to critically evaluate solutions proposed for different problems, and to correctly interpret the related topics.

Communication skills

At the end of the course, the student must have acquired a good ability to clearly communicate considerations concerning problems of financial mathematics. The working mode is shown in the classroom during lessons and during the exercises.

Learning skills

At the end of the course the student must have acquired a good degree of autonomy in the study of discipline, reading and interpretation of financial data, in the search for useful information to deepen the knowledge of the discussed topics.

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

or in alternative:

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


The exam consists of two written tests. A practical test consisting of 3 exercises to be carried out in an hour and a half. A student is allowed to the theory test if the practical test is passed with a minimum score of 16/30. The second part of the exam can take place in the same day or in any examination day within one year. The theory test consists of four open questions concerning the points listed in the program and assessing from 0 to 7.5 points each question. The final rating is determined by considering both the exercises and the theory test. The assessment of each answer is based on the different levels of knowledge of the subject matter: the knowledge of the meaning and the computation procedure and its correct application in the subject matter, the knowledge of theoretical arguments and proofs leading to the results.

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