Financial Mathematics (FSI-SFI)

Academic year 2020/2021
Supervisor: RNDr. Pavel Popela, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The basic concepts and models of financial problems are accompanied by the theory and simple examples.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Attendance of students is required and checked by students’ activity. Missed lessons are compensated by additional assignments.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture 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 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.
Literature - fundamental:
1. Dupačová,J. et al.: Stochastic Models for Economics and Finance, Kluwer, 2003.
2. Brandimarte, P.: Numerical Methods in Finance: A MATLAB-Based Introduction. 1st edition, Wiley - Interscience, 2001.
Literature - recommended:
1. Cipra, T. Finanční matematika v praxi, HZ 1993
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2A-P full-time study M-MAI Mathematical Engineering -- GCr 4 Compulsory 2 2 W