Course detail

Financial Mathematics

FSI-SFI-AAcad. year: 2022/2023

The course presents basic financial models. It focuses on main concepts and computational methods. Several lectures are especially developed to make students familiar with optimization models.

Language of instruction

English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

RNDr. Pavel Popela, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

The course is designed for students of mathematical engineering and is useful
for students of applied sciences. The fundamental knowledge of financial models is presented.

Prerequisites

The knowledge of Calculus and Linear Algebra together with probabilistic and statistical methods (including time series) as well as optimisation techniques within the framework of SOP and SO2 courses is required.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Graded course unit credit is awarded on the basis of a written exam and the discussion in the group of participating students.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The basic concepts and models of financial problems are accompanied by the theory and simple examples.

Specification of controlled education, way of implementation and compensation for absences

Attendance of students is required and checked by students’ activity. Missed lessons are compensated by additional assignments.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brandimarte, P.: Numerical Methods in Finance: A MATLAB-Based Introduction. 1st edition, Wiley - Interscience, 2001. (EN)
Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003. (EN)

Recommended reading

Brandimarte, P.: Numerical Methods in Finance: A MATLAB-Based Introduction. 1st edition, Wiley - Interscience, 2001. (EN)
Capinski, M., Zastawniak, T.: Mathematics for Finance: An Introduction to Financial Engineering. Springer Verlag, 2003. (EN)
Cipra T.: Financial and Insurance Formulas, Springer-Verlag, 2010. (EN)
Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003. (EN)

Classification of course in study plans

  • Programme N-MAI-A Master's 2 year of study, winter semester, compulsory
  • Programme N-AIM-A Master's 2 year of study, winter semester, compulsory

  • Programme LLE Lifelong learning

    branch CZV , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

1. Basic concepts, money, capital and securities.
2. Simple and compound interest rate, discounting.
3. Investments, cash flows and its measures, time value of money.
4. Assets and liabilities, insurance.
5. Bonds, options, futures, and forwards.
6. Exchange rates, inflation, indices.
7. Portfolio optimization - classical model.
8. Postoptimization, risk, funds.
9. Twostage models in finance.
10. Multistage models in finance.
11. Scenarios in financial mathematics.
12. Modelling principles, identification of dynamic data.
13. Discussion on advanced stochastic models.

Computer-assisted exercise

13 hod., compulsory

Teacher / Lecturer

RNDr. Pavel Popela, Ph.D.

Syllabus

Selected examples and exercises illustrating:
1. Basic concepts, money, capital and securities.
2. Simple and compound interest rate, discounting.
3. Investments, cash flows and its measures, time value of money.
4. Assets and liabilities, insurance.
5. Bonds, options, futures, and forwards.
6. Exchange rates, inflation, indices.
7. Portfolio optimization - classical model.
8. Postoptimization, risk, funds.
9. Twostage models in finance.
10. Multistage models in finance.
11. Scenarios in financial mathematics.
12. Modelling principles, identification of dynamic data.
13. Discussion on advanced stochastic models.

Course participance is obligatory.