VŠTE:NE_AMA Applied Mathematics - Course Information

NE_AMA Applied Mathematics

Extent and Intensity

2/1/0. 4 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Jiří Čejka, Ph.D. (seminar tutor)
doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
Ing. Tadeáš Říha (seminar tutor)

Guaranteed by

doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice

Timetable of Seminar Groups

NE_AMA/NE6: Sat 19. 10. 8:00–9:30 B2, 9:40–11:10 B2, 11:25–12:55 B2, Sun 3. 11. 13:05–14:35 B3, 14:50–16:20 B3, 16:30–18:00 B3, J. Čejka
NE_AMA/P01: each odd Monday 16:30–18:00 B1, each odd Monday 18:10–19:40 B1, J. Čejka
NE_AMA/S01: Tue 8:00–8:45 B5, J. Čejka
NE_AMA/S02: Tue 8:45–9:30 B5, J. Čejka

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives supported by learning outcomes

The course focuses on advanced mathematical methods used in financial theory. The aim is to become familiar with the sequences and series, principles of time value of money, and basic principles of financial markets.

Learning outcomes

After successful completion of the course, students are able to:
- use sequences in solving mathematical problems,
- work with time series, add and analyse their convergence,
- use various types of interests with different frequencies,
- set effective and real interest rate,
- calculate the current and future value of annuity, prepare a plan of debt redemption,
- use mathematical procedures in evaluating determinist cash flow,
- value bonds, stocks, and work with exchange rates,
- carry out a sensitivity analysis of bond prices to interest rate change (duration, convexity),
- analyse revenue and portfolio risk.

Syllabus

• Lectures
• 1. Basic terms of financial mathematics, sequences and series, summation of series.
• 2. Interest. Types of interest. Simple interest method, decursive interest, basic equations. Discount.
• 3. Compound interest, basic equations. Combined interest. Calculation of interest rate and interest.
• 4. Short-term and long-term savings.
• 5. Pensions as regular payments from the investment, repayment of load with a constant annuity, amortization.
• 6. Note payables and note payables trade. Discount. Checking accounts. Mortgage loans. Consumer credit. Forfaiting, factoring and leasing.
• 7. Bonds, duration, convexity, immunization.
• 8. Shares, foreign exchange trading, financial trade and futures, portfolio performance, two- and multi-component portfolio.
• 9. Exchange rates.
• 10. Introduction to time series analysis, rolling average, difference and growth index.
• 11. Modelling of time series, time series components.
• 12. Trend component, models of trend components.
• 13. Application of time series for forecasting.
  Seminars
• 1. Basic terms of financial mathematics, sequences and series.
• 2. Simple interest method, decursive interest, basic equations, discount.
• 3. Compound interest, combined interest, interest rate, interest.
• 4. Short-term and long-term savings, using summation of series.
• 5. Pensions, loan, loan repayment, amortisation.
• 6. Note payables and note payables trading, mortgage loans, consumer credit.
• 7. Valuation of bonds.
• 8. Shares, foreign exchange trading, financial trade and futures, portfolio performance, multi-component portfolio.
• 9. Exchange rates.
• 10. Introduction to time series analysis, time series components.
• 11. Modelling of time series.
• 12. Trend component, models of trend components.
• 13. Using time series for forecasting.

Literature

required literature
• PROUZA, L., 2007. Finanční a pojistná matematika. Praha: Vysoká škola ekonomie a managementu. ISBN 978-80-86730-17-2.
• ŠOBA, O., M. ŠIRŮČEK a R. PTÁČEK, 2013. Finanční matematika v praxi. Praha: Grada. ISBN 978-80-247-4636-4.

recommended literature
• JÍLEK, J., 2013. Finance v globální ekonomice II – Měnová a kurzová politika. Praha: Grada. ISBN 978-80-247-8822-7
• RADOVÁ, J., P. DVOŘÁK a J. MÁLEK, 2013. Finanční matematika pro každého. 8., rozš. vyd. Praha: Grada. ISBN 978-80-247-4831-3.
• CIPRA. T., 2006. Pojistná matematika: teorie a praxe. Praha: Ekopress. ISBN 80-86929-11-6.
• ŠOBA O., M. ŠIRŮČEK a R. PTÁČEK, 2017. Finanční matematika v praxi. 2. vyd. Praha: Grada. ISBN 978-80-271-0250-1.
• RADOVÁ, J., J. MÁLEK, P. JABLONSKÝ a M. RADA, 2011. Finanční matematika pro každého – příklady + CD-ROM. Praha: Grada. ISBN 978- 80-247-3584-9.
• CIPRA, T., 2008. Finanční ekonometrie. Praha: Ekopress. ISBN 978-80- 86929-43-9.
• EPPING, R. CH., 2004. Průvodce globální ekonomikou. Praha: Portál. ISBN 978-80-7178-825-6.
• ARLT, J. a M. ARTLOVÁ, 2009. Ekonomické časové řady. Praha: Professional Publishing. ISBN 978-80-86946-85-6.
• DOŠLÁ, Z. a P. LIŠKA, 2014. Matematika pro nematematické obory. Praha: Grada. ISBN 978-80-247-5322-5.
• ARLT, J., M. ARLTOVÁ a E. RULÍKOVÁ, 2004. Analýza ekonomických časových řad s příklady, 2. vyd. Praha: Vysoká škola ekonomická, Oeconomica. ISBN 80-245-0777-3.

Forms of Teaching

Lecture
Seminar
Exercise
Professional Practice
Tutorial
Consultation

Teaching Methods

Frontal Teaching
Group Teaching - Cooperation
Project Teaching
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies

Student Workload

Activities	Number of Hours of Study Workload
	Daily Study	Combined Study
Preparation for the Mid-term Test	10
Preparation for Lectures	13
Preparation for Seminars, Exercises, Tutorial	13	40
Preparation for the Final Test	10	26
Samostudium (in Czech)	11	25
Attendance on Lectures	26
Attendance on Seminars/Exercises/Tutorial/Excursion	13	13
Test – mid-term, test final	8
Total:	104	104

Assessment Methods and Assesment Rate

Test – final 70 %
2 continuous tests (2x 15 points) 30 %

Exam conditions

For successful completion of the course it is necessary to achieve at least 70 % of the course and final test together under the conditions specified below. In the course test, students can get up to 30 points, i.e. 30 %. In the final test, students can get up to 70 points, i.e. 70 %. Grading for the course, i.e. points for the final test (70 - 0) + points for the course test (30 - 0): A 100 – 90, B 89.99 – 84, C 83.99 – 77, D 76.99 – 73, E 72.99 – 70, FX 69.99 – 30, F 29.99 – 0. Students in the full-time form of study are obliged to participate in 70 % of the lessons (except for lectures).

Course test: 2 course tests (2x 15 points) – 30 points

Final test: Final test – 70 points (i.e. 70 %)

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.

Teacher's information

Attendance in the course is defined in a separate VSTE internal standard (Evidence of student attendance at VSTE) for all forms of study. Students in full-time form of study are obliged to attend at least 70 % of the lessons (except for the lectures).

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