FINANCIAL MATHEMATICS (SEM)
Learning outcomes of the course unit
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);
- Structure of returns and prices of fixed-income securities.
He will learn how to use such models and methods.
The models dealt with are deterministic. The student also examines simple models dealing with 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.
The course aims at developing the financial sensibility and the ability for critical analysis which are expected from a student graduated in the economic area, and who is employed in the financial sector, or deals with the financial management of commercial or industrial enterprises.
The student is educated in the use of the basic financial-quantitative language. He/she is able to interpret (and, if necessary, validate by developing autonomously 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.
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.
Although not compulsory, a basic knowledge of the contents of Calculus is recommended.
Course contents summary
- 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. Mean duration. Interest rate risk. Financial immunization.
Available online, on the Elly platform. During the teaching period, the detailed program will be updated 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, available online on the Elly platform, or (when allowed to get into the Department) in printed version at the copy centre of the Department of Economics and Management.
Online lectures, on Teams and Elly platforms. Some lectures will be asynchronous (videos will be available at links published on Elly), while some others will be synchronous (live meetings via Teams). Roughly, the asynchronous lectures will be devoted to exposing the conceptual and theoretical features of the models, while the synchronous ones will examine applications to practical problems through exercises. The synchronous lectures (live) will include both face-to-face expositions and moments of interaction with students. 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 in the section about evaluation. The detailed timetable of the classes (also telling apart synchronous and asynchronous ones) is available on the course page on Elly.
The slides used during classes are available since the beginning of the course online on the Elly Platform or (when the Department will be accessible again) in printed version at the copy centre of the Department of Economics and Management.
Live recordings of the synchronous lectures will be available online after their conclusion. The videos of the asynchronous lectures and the recordings of the synchronous ones will be available for a limited time only; the availability period of each video will be specified in the detailed classes plan available on Elly. Students are warmly encouraged to take the lessons in accordance with the classes' traditional timetable.
Assessment methods and criteria
Multiple choice tests, available time 20', possibly followed (upon request) by an addendum. The multiple choice test consists in 15 questions, 5 for each part of the course. Each correct answer is worth 2 points, wrong answers are worth -0.5 points. Given its simplified nature, the maximum grade attainable with the multiple choice test is 25/30.
Students who pass the test with a grade between 22 and 25 can ask to take an addendum of examination, which will consist in a short exercise and some questions to theoretical questions, where they will have to show a deeper insight and a greater mastering (with respect to the test) of the course contents. The final grade will be based on the preparation shown in the addendum only, so that the exam could be passed (with a grade between 18 and 30 cum laude) or failed, with no guarantee that the final mark will be at least equal to the test.
As long as the exams take place online, the tests will be held through Zoom (or Teams) and Elly/Respondus platforms, and the addendum will be oral (through Zoom or Teams). The addendum will take place the same day of the test, or in the immediately following days. When the exams will be back to take physically place in the Department, the test will still be held online (students will bring their own devices) or in written form (for students who shall not manage to access the online resources from the Department rooms). The addendum will either be written or oral, and will take place after the results of the test will be published.
The questions of the test and of the addendum will be conceived so as to assess knowledge and comprehension of the course topics. Some questions will be written in an original way with respect to the didactical 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 telling the right answers, students will have to prove their knowledge and mastering of technical language.
During the exam, a pocket calculator can be used. No other device is admitted (unless needed to access the online test). The exam is "closed-book": consultation of teaching materials is not allowed.
Honor grade ("laude") may be awarded to students who, besides obtaining full marks, in taking the addendum showed a particular in-depth knowledge and a relevant overall vision of the subject, together with an excellent ability in applying the gained knowledge, a relevant independence of judgment and a particular care in drafting their assignment.
Grades are published in Esse3 within some days from the exam.
Within the teaching period, six partial assessments will be organized, each lasting 6' and composed by 3 multiple choice questions. Each correct answer is worth 2 points, wrong answers are worth -0.5 points. The final mark is the sum of the score obtained in each test, with a maximum grade of 27; the exam is passed with a grade of 18 or above (there is no need to take part to all tests). Students who pass with a grade above 25 can ask for an addendum of examination, to be taken after the last test, perfectly analogous to the addendum for the ordinary sessions. During the partial assessments it is possible to consult teaching materials (textbook, slides, and so on); nevertheless, the available time is limited, so that we strongly suggest students not to waste it.