# FINANCIAL MATHEMATICS (SEM) cod. 16785

2° year of course - First semester
Professor
- Gino FAVERO
Metodi matematici dell'economia e delle scienze attuariali e finanziarie (SECS-S/06)
Field
Statistico-matematico
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in ITALIAN

## 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, entreprises, and so on);
- term structure of returns and prices of fixed-income securities.
The course deals with deterministic models only. The student also examines simple models for investments bearing financial risks, with particular regard to financial immunization with respect to 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.

Independence of judgment
The course aims at developing the financial sensibility 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 entreprises.

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 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.

## Prerequisites

Being acquainted with the basic topics of Calculus course, even if it is not compulsory to pass the related exam, is definitely useful in order to better understand the methodologies of Financial mathematics.

## Course unit content

Part 1: future and 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 in the case of modifications.

## Bibliography

- 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 and numerical exercises, available online on the Elly platform, or in printed version at the copy centre of the Department of Economics and Management.

- Multiple choice questions, available online on the Elly platform.

## Teaching methods

Face-to-face lectures.

Lectures will be recorded, the url of the recordings will be published on Elly. If the recording fails, a replacement video will be provided. In order to stimulate an active participation in class, some introductory videos may be provided, to be watched before the related lecture. Detailed information wil be provided on Elly.

In order to encourage active participation to the course, some problems will be proposed, to be autonomously solved at home outside lection hours, so that the students will have the chance to engage in autonomous application of the concepts introduced in class. Moreover, ongoing tests will be assigned, which will add up to the final grade of the exam; details are available on Elly

The slides used during classes are available since the beginning of the course online on the Elly Platform or in printed version at the copy centre of the Department of Economics and Management.

## 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 (both for mathematics and for 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 (multicple 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.

Where exams take place: at the time this syllabus is written, the exams have to be taken on site. Any change will be promptly communicated.

Oral

No oral exam is usually planned. Students who get a final grade of 27/40 or above can nevertheless ask to take an oral exam. Furthermore, teachers 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. Teachers 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 with respect to the level expected for 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.

Generalities

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.

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