cod. 16785

Academic year 2023/24
2° year of course - First semester
Annamaria OLIVIERI
Academic discipline
Metodi matematici dell'economia e delle scienze attuariali e finanziarie (SECS-S/06)
Type of training activity
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit

Learning objectives

Knowledge and understanding:
The student learns 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);
- Term-structure of returns and prices of fixed-income securities.
He/she will learn how to use such models and methods.
The course deals with deterministic models only. The student also examines simple models for investments bearing financial risks, with particular regard to financial immunization in respect of interest rate risk.

Applying knowledge and understanding:
The student is 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.

Making judgements:
The course aims at developing the financial sensitivity and the ability for critical analysis which are expected from a student graduated in business economics and management, and who is employed in the financial sector, or deals with the financial management of commercial or industrial enterprises.

Communication skills:
The student is educated in the use of the basic financial-quantitative language. He/she is able to interpret (and, if necessary, validate by autonomously developing appropriate calculations) the output of basic financial packages, as well as to describe them to third parties (such as users of financial services). Moreover, he/she is able to understand and describe the basic quantitative financial valuation criteria, commonly used for financial decision-making.

Learning skills:
The student develops the ability to understand the financial problems and to select the most appropriate quantitative valuation models. The student learns how to adopt deterministic quantitative models, also in a stochastic framework. In this latter respect, he/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.


It is not compulsory to have passed the exam of Calculus to take the exam of Financial mathematics. However, a basic knowledge of the contents of Calculus is recommended, so to better understand the methodologies of Financial mathematics.

Course unit content

Part 1: Future value, present value. The valuation of annuities. Mortgages.
Part 2: Net Present Value, Internal Rate of Return. Net Present Value and Economic Value Added.
Part 3: Price and yield to maturity of fixed-interest bonds. The term structure of interest rates (spot rates and forward rates). The non-arbitrage valuation principle.
Part 4: Mean duration. Interest rate risk. Financial immunization.

Full programme

Available online, on the Elly platform. During the teaching period, the detailed program will be updated at least weekly.


In Italian: Samuel A. Broverman (2019). Matematica finanziaria. Edizione italiana a cura di A. Olivieri e G. Favero. Egea, Milano
In English: Samuel A. Broverman (2017). Mathematics of Investment and Credit. ACTEX Learning.

Course slides, numerical exercises and multiple choice questions, available online on the Elly platform.

Teaching methods

Face-to-face lectures will be recorded; the url will be provided on Elly. In order to stimulate active participation in class, for some lectures a pre-recording could be provided, to be listened before the face-to-face lecture. For detailed information, see Elly. If, because of technical issues, the recording of live lectures fails, a replacement video will be provided.
The student has to further practice on models and numerical problems on his/her own. The student will be assigned problems which he/she has to solve autonomously after classes, so to develop his/her own ability to use the models presented during classes.
Moreover, mid-term tests will be assigned, which will add up to the final grade of the exam; details are available on Elly.

Assessment methods and criteria

Multiple choice test + short numerical exercises.

Multiple choice questions: 9 questions (3 on future value, present value, annuity value, loans; 2 on financial evaluations, Net Present Value, Internal Rate of Return, Economic Value Added; 2 on price and yelad to maturity of fixed-interest bonds, term structure of interest rates, no-arbitrage principle; 2 on mean duration, interest rate risk, financial immunization). Each question is worth 2.5 points if correct, -0.5 points if wrong, 0 points if blank; the maximum overall score is 20 points.

Short numerical exercises: 5 questions (2-1-1-1-1 in the same categories as above), asking to solve a short numerical problem, possibly providing a financial interpretation. Each answer will be graded from -1 to 3 points, depending on accuracy, efficiency of the chosen models and properness of the language used (mathematical language and financial interpretation).

The final grade of the exam is the sum of the scores obtained in the two parts. Honor grades will not be awarded on a predefined rule, but rather on evidence of a particular in-depth knowledge and a relevant overall vision of the subject, both in terms of language and of models.

Time available for the test (multiple choice questions + numerical exercises): 40 minutes.

The exam is open-book: it is possible to use a pocket calculator and to browse the teaching material (in printed form) used to train for the exam. Neither using other electronic devices, nor interacting with other people in any form, are allowed.


No oral exam is usually planned. Students who get a final grade of 27/30 or above can nevertheless ask to take an oral exam. Furthermore, lecturers can require a student to undertake an oral exam in order to investigate on the answers to her/his test.

The oral exam usually adds +/- 3 points to the final grade of the test. Lecturers may nevertheless subtract more than 3 points to the final grade if the student shows a significant lack of knowledge.

Content of the oral exam: numerical exercise and theoretical questions. The student must prove more in-depth knowledge than what is possible to check in the written test.

During the oral exam it is possible to use a pocket calculator; apart from that, the exam is closed-book.

Mid-term tests

During the teaching period, 4 online mid-term tests and a final on site written test will be organized. The final test will take place on the first exam date of the winter session.

The detailed description of the mid-term tests is available on Elly.

The questions of the test will be conceived so as to assess knowledge and understanding of the course topics. Some questions will be written in an original way with respect to the teaching materials, in order to assess the capability to learn and to enforce knowledge into solving problems. Independence of judgment will be ascertained by asking the interpretation of some numerical results. In chosing the right answers to multiple choice questions, as well as in providing the algebraic and wording formulation of numerical exercises, the student will have to prove his/her knowledge and mastering of technical language.

Grades are published on Esse3 platform within some days from the exam, barring unforeseen circumstances.

Other information