Financial Mathematics II

  • Credits: 5
  • Ending: Examination
  • Range: 2P + 2C
  • Semester: winter
  • Year: 1
  • Faculty of Economic Informatics

Teachers

Included in study programs

Actuarial Science

Teaching results

Completion of the course Financial Mathematics II presupposes the development of financial thinking over time.
Knowledge
Progress in the field of new knowledge is evident after completing the course. Students will understand the valuation of loans represented by fixed interest securities with a focus on matching the assets and liabilities of the insurance company's technical reserves. They will gain knowledge about the operation of futures trading instruments with a focus on trading strategies.
Competences
Based on the above knowledge, students are able to comment on the selection of assets with a fixed coupon and then compile a requirement for the construction of a portfolio of technical reserves of the insurance company with a focus on its immunization.
Skills
As part of the educational process, they will acquire such skills that will enable students to make a selection of long-term securities with a focus on matching with liabilities. Get acquainted with the functioning of futures contracts at futures contracts.

Indicative content

1. Accumulation and discount factors, inflation on projects, low start of loan repayment
2. Fixed interest securities, Makeham's formula, yield and maturity
3. Loan valuation, interest and capital tax, profitability
4. Optimal loan maturity and capital gains tax, loss compensation
5. Time structure of interest rates, spot, forward interest rate, yield curve
6. Average project maturity, volatility of fixed interest securities
7. Matching of assets and liabilities, Redington's theory of immunization, full immunization
8. Futurity and forward contracts, short and long positions, clearing houses
9. Term price of a security, value of a forward contract, short position risk
10. Swaps, matching payments, capital resources while reducing costs
11. Options, payout function, internal and time value of options, option price limits
12. Put-call parity. Black – Scholes model and partial differential equation.
13. Option and stock strategies, trading strategies: synthetic contract, bear and bull spreed

Support literature

1. Garrett, S. J.: An Introduction to the Mathematics of Finance. Oxford: Elsevier, Butterworth –Heinemann, 2013, ISBN: 978-0-08-098240-3
2. Pinda, Ľ.: Deriváty cenných papierov /Vybrané problémy/. IURA EDITION 2001. ISBN 80-88715-98-9
3. Hull, J. C.: Options, futures, and other derivative securities. 11-th Edition. Prentice-Hall International, Inc. 2018. ISBN-13: 978-0-13-6940104
4. Pinda, Ľ.: Finančná matematika I. Letra Edu 2021, ISBN: 978-80-89962-82-2
5. Pinda, Ľ.: Finančná matematika investičných projektov. Bratislava: IURA EDITION, spol. s r.o. 2010, ISBN: 978-80-8078-319-8
6. Melicherčík, I.– Olšanová, L.–Úradníček, V.: Kapitoly z finančnej matematiky. EPOS 2005. ISBN 80-8057-651-3

Syllabus

1. Accumulation and discount factors, inflation on projects, low start of loan repayment 2. Fixed interest securities, Makeham's formula, yield and maturity 3. Loan valuation, interest and capital tax, profitability 4. Optimal loan maturity and capital gains tax, loss compensation 5. Time structure of interest rates, spot, forward interest rate, yield curve 6. Average project maturity, volatility of fixed interest securities 7. Matching of assets and liabilities, Redington's theory of immunization, full immunization 8. Futurity and forward contracts, short and long positions, clearing houses 9. Term price of a security, value of a forward contract, short position risk 10. Swaps, matching payments, capital resources while reducing costs 11. Options, payout function, internal and time value of options, option price limits 12. Put-call parity. Black – Scholes model and partial differential equation. 13. Option and stock strategies, trading strategies: synthetic contract, bear and bull spreed

Requirements to complete the course

30% written work,
70% written exam.

Student workload

Total study load (in hours): 156 hours
26 hours of lectures,
26 hours of exercise,
52 hours of self-study in preparation for the exam,
13 hours preparation for seminars,
13 hours preparation for written work.

Language whose command is required to complete the course

slovak

Date of approval: 10.02.2023

Date of the latest change: 15.05.2022