B_FIM Financial and Investment Mathematics

University of Finance and Administration
Summer 2024
Extent and Intensity
2/1/0. 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
PaedDr. Renata Majovská, PhD.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Ivana Plačková
Timetable of Seminar Groups
B_FIM/cEKKV: Fri 16. 2. 10:30–11:14 KV202, 11:15–12:00 KV202, 12:15–12:59 KV202, 13:00–13:45 KV202, Fri 15. 3. 10:30–11:14 KV202, 11:15–12:00 KV202, 12:15–12:59 KV202, 13:00–13:45 KV202, Fri 12. 4. 10:30–11:14 KV202, 11:15–12:00 KV202, 12:15–12:59 KV202, 13:00–13:45 KV202, R. Majovská
B_FIM/cEKPH: each even Wednesday 15:45–16:29 E227, each even Wednesday 16:30–17:15 E227, R. Majovská
B_FIM/cFPH: each even Wednesday 17:30–18:14 E307, each even Wednesday 18:15–19:00 E307, except Wed 21. 2., except Wed 6. 3., except Wed 20. 3., except Wed 3. 4., except Wed 17. 4. ; and Wed 21. 2. 17:30–19:00 E227, Wed 6. 3. 17:30–19:00 E227, Wed 20. 3. 17:30–19:00 E227, Wed 3. 4. 17:30–19:00 E227, Wed 17. 4. 17:30–19:00 E227, 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 20. 2., except Tue 16. 4. ; and Fri 8. 3. 12:15–13:45 KV202, 14:00–15:30 KV202, Fri 5. 4. 12:15–13:45 KV205, 14:00–15:30 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 20. 2., except Tue 16. 4. ; and Fri 8. 3. 12:15–13:45 E230, 14:00–15:30 E230, Fri 5. 4. 12:15–13:45 E230, 14:00–15:30 E230, P. Budinský
B_FIM/vEKFPH: Fri 23. 2. 17:30–19:00 E225, 19:15–20:45 E225, Fri 22. 3. 14:00–15:30 E225, 15:45–17:15 E225, Sat 13. 4. 9:45–11:15 E225, 11:30–13:00 E225, 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
The aim of the course is:
- explain the concepts of interest
- 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 and convexity
- 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
Learning outcomes
At the end of this course the student will be able to:
- understand and explain simple and compound interest
- use knowledge on the calculation of the basic characteristics of bonds (yield, price, duration, convexity)
- explain the principles of neutralization bond portfolio
- build the portfolio of equities and derivatives
- describe the basic strategy of investing in portfolios
Syllabus
  • 1. Interest rate. Simple and compound interest, frequency of interest. Continuous interest. Yield, present and future value, discounting. Calculation of the present value of the investment.
  • 2. Calculation of income at a fixed present and future value, recalculation of income at different frequency of interest.
  • 3. Classification of bonds. Bond face value, coupon rate, bond yield. Bond price calculation for zero-coupon bond, annuity and perpetuity.
  • 4. Rules for counting bonds. The relationship between bond price and yield. Relationship between coupon rate and bond yield. 5. Aliquot interest yield, gross and net price of the bond. Calculation of the net price of the bond.
  • 6. Bond price sensitivity to yield changes. Modified and Macaulay duration, bond convexity and their properties and calculation.
  • 7. Investment in bonds. Reinvestment and capital risk. Duration and investment horizon.
  • 8. Bond portfolio, its duration and convexity. Building a bond portfolio for a predetermined duration equal to the investment horizon.
  • 9. Stock portfolio, its construction, unique and market risk.
  • 10. Markowitz model, set of admissible portfolios.
  • 11. Derivative portfolio I - forward contracts and options, basic income graphs depending on the price of the underlying asset.
  • 12. Derivative portfolio II - spread, combination and hedging strategies.
Literature
    required literature
  • Budinský, P. : Finanční a investiční matematika. Praha : VŠFS, 2016.
    recommended literature
  • Šoba, O., Širůček, M.: Finanční matematika v praxi. Praha: Grada, 2017
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% in tutorials in part-time study. Students with lower than required participation have to fulfill additional study duties.
Students with ISP have the same duties. Compulsory attendance is not required.
Assessment methods
Method of completion: in order to be awarded credit, it is necessary to successfully write a credit test (51% of points) and 75% participation in the exercise, for the exam, you must successfully write an examination test (51% of correct answers) and take 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 2023, Summer 2025.
  • Enrolment Statistics (Summer 2024, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/summer2024/B_FIM