B_FIM Financial and Investment Mathematics

University of Finance and Administration
Summer 2023
Extent and Intensity
2/1. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Petr Budinský, CSc. (seminar tutor)
PaedDr. Renata Majovská, PhD. (seminar tutor)
Guaranteed by
doc. RNDr. Petr Budinský, CSc.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Ivana Plačková
Timetable of Seminar Groups
B_FIM/cEKKV: Fri 17. 2. 8:45–9:29 KV204, 9:30–10:15 KV204, 10:30–11:14 KV204, 11:15–12:00 KV204, Fri 17. 3. 8:45–9:29 KV204, 9:30–10:15 KV204, 10:30–11:14 KV204, 11:15–12:00 KV204, Fri 14. 4. 8:45–9:29 KV204, 9:30–10:15 KV204, 10:30–11:14 KV204, 11:15–12:00 KV204, R. Majovská
B_FIM/cEKPH: each even Thursday 8:45–9:29 E224, each even Thursday 9:30–10:15 E224, R. Majovská
B_FIM/cFPH: each even Thursday 10:30–11:14 E225, each even Thursday 11:15–12:00 E225, R. Majovská
B_FIM/poEKKV: each even Tuesday 8:45–9:29 KV205, each even Tuesday 9:30–10:15 KV205, each even Tuesday 10:30–11:14 KV205, each even Tuesday 11:15–12:00 KV205, except Tue 4. 4. ; and Tue 4. 4. 8:30–10:00 KV205, 10:15–11:45 KV205, P. Budinský
B_FIM/pxEKFPH: each even Tuesday 8:45–9:29 E230, each even Tuesday 9:30–10:15 E230, each even Tuesday 10:30–11:14 E230, each even Tuesday 11:15–12:00 E230, except Tue 4. 4. ; and Tue 4. 4. 8:30–10:00 E230, 10:15–11:45 E230, P. Budinský
B_FIM/vEKFPH: Fri 10. 2. 14:00–15:30 E224, 15:45–17:15 E224, Fri 10. 3. 14:00–15:30 E224, 15:45–17:15 E224, Fri 24. 3. 14:00–15:30 E224, 15:45–17:15 E224, R. Majovská
Prerequisites
There are no prerequisites for this course.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of this course the student will be able to understand and explain simple and compound interest. They will also acquire knowledge on the calculation of the basic characteristics of bonds (yield, price, duration, convexity), learn to build the portfolio of equities and derivatives  . At the end of this course the student will be able to:
- Explain the concepts of interest, annual interest rate
- Describe different types and kinds of interest
- Calculate the future and present value of the investment and its return
- Explain the concept of bond, including the rules for counting and valuation
- Explain and calculate the duration
- Explain the principles of neutralization bond portfolio
- Establish a portfolio composed of two bonds
- Explain the principles of the derivatives and their use
- Describe the basic strategy of investing in portfolios
Syllabus (in Czech)
  • 1. Úroková sazba. Jednoduché a složené úročení, frekvence úročení. Spojité úročení. Výnos, současná a budoucí hodnota, diskontování. Výpočet současné hodnoty investice.
  • 2. Výpočet výnosu při pevně zadané současné a budoucí hodnotě, přepočet výnosů při různé frekvenci úročení.
  • 3. Klasifikace dluhopisů. Nominální hodnota dluhopisu, kuponová sazba, výnos dluhopisu. Výpočet ceny dluhopisu pro bez-kupónový dluhopis, anuitu a perpetuitu.
  • 4. Pravidla pro počítání s dluhopisy. Závislost mezi cenou a výnosem dluhopisu. Vztah mezi kuponovou sazbou a výnosem dluhopisu. 5. Alikvotní úrokový výnos, hrubá a čistá cena dluhopisu. Výpočet čisté ceny dluhopisu.
  • 6. Citlivost ceny dluhopisu na změnu výnosu. Modifikovaná a Macaulayova durace, konvexita dluhopisu a jejich vlastnosti a výpočet.
  • 7. Investice do dluhopisů. Reinvestiční a kapitálové riziko. Durace a investiční horizont.
  • 8. Dluhopisové portfolio, jeho durace a konvexita. Sestavení dluhopisového portfolia pro předem zadanou duraci rovnou investičnímu horizontu.
  • 9. Akciové portfolio, jeho konstrukce, jedinečné a tržní riziko.
  • 10. Markowitzův model, množina přípustných portfolií.
  • 11. Derivátové portfolio I - forwardové kontrakty a opce, základní grafy výnosů v závislosti na ceně podkladového aktiva.
  • 12. Derivátové portfolio II - strategie typu spread, kombinace a zajišťování.
Literature
    required literature
  • Budinský, P. : Finanční a investiční matematika. Praha : VŠFS, 2016.
Teaching methods
- lectures and seminars in full-time study, - tutorials in part-time study, Minimal required participation is 75% on seminars in full-time study and 50% on tutorials in part-time study. Students with lower than required participation have to fulfill additional study duties.
Assessment methods
Method write endings class exam and 75% participation in exercises, to try to be successful (50% correct answers) write exam exam, and do an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Information on the extent and intensity of the course: 12 hodin KS/semestr.
The course is also listed under the following terms Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, summer 2012, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Summer 2021, Summer 2022, Summer 2024, Summer 2025.
  • Enrolment Statistics (Summer 2023, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/summer2023/B_FIM