Teaching code

4S00393

Academic staff

Cosimo Munari, Cecilia Mancini

Coordinator

Cosimo Munari

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Primo semestre L dal Sep 21, 2026 al Jan 15, 2027.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The objectives of the course are the introduction of the pillars of financial contracts and the quantitative method for their management, to be developed to the foundations of fixed income and portfolio management. The course will introduce the basic jargon in finance, as well as the main concepts underlying asset valuation and assessment of risk. At the same time, the course will develop quantitative methods, which will be useful for advanced courses in finance.
At the end of the course, the student is expected to be able to perform operations involving the financial instruments explained in class, and to understand the theoretical ideas illustrated in the course.
Basic knowledge of mathematics and statistics is strongly recommended.

Prerequisites and basic notions

Students are expected to be familiar with some basic notions of mathematics including: real functions of one or more real variables, elementary functions (powers, exponentials, logarithms), their properties (in particular monotonicity, continuity, differentiability), derivatives of elementary functions, derivatives of the sum of functions, of the difference, of the product, of the quotient, of compositions.

Program

The course is split into the following modules:
1. Financial activities under certainty
1.1 Financial activities
1.2 Financial laws
1.3 Compounded activities
1.4 Properties of financial laws
1.5 Annuities, PAC
1.6 Amortization of a debt and other compounded activities
1.7 Internal rate of return
1.8 Numerical methods to solve equations
2. The bond market
2.1 Perfect markets and the no-arbitrage principle
2.2 Fair price of a bond
2.3 Term structure of the ZCB prices
2.4 Term structure of the interest rates
2.5 The variable rate mortgage
2.6. Interest rate risk: duration, financial immunization, ALM
3. Models for the stock market
3.1. Random financial activities: risk and return
3.2. Portfolio selection models: the mean-variance approach
3.3. Link with the Capital Asset Pricing Model
3.4. Stock valuation models

Bibliography

Didactic methods

The course aims to introduce the main quantitative models for the analysis, valuation, and management of financial assets, and provides the fundamentals for the quantitative study of bond and equity finance. Students will learn the appropriate terminology and concepts to understand and apply the tools of financial mathematics. Critical skills in describing and developing basic financial models will be fostered, with particular attention to managing the risk-return profile of a financial asset. At the same time, the course develops the main quantitative methodologies useful as a basis for participation in advanced finance courses.

Learning assessment procedures

The exam consists of a written test featuring two modules, each corresponding to the program covered by the two lecturers. To pass a module it is necessary to score a grade of at least 16/30. To pass the entire test it is necessary to score a grade of at least 18/30, computed as the weighted average of the grades of each module. The weights are proportional to the teaching load of the lecturers. In case a single module is passed, the grade can be accepted and retained for the entire academic year.

Evaluation criteria

The ability to solve the exercises, the knowledge of the basic definitions, the awareness of the relationships between basic concepts and the financial interpretation will be considered fundamental.

Criteria for the composition of the final grade

The grade is expressed in a scale from 0 to 30. The exam is passed if the grade is at least equal to 18/30.

Exam language

Italiano