N_MaMF Mathematic models in financial sphere

University of Finance and Administration
Winter 2017
Extent and Intensity
2/1. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Ing. Jaroslav Brada, Ph.D. (seminar tutor)
doc. RNDr. Petr Budinský, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Petr Budinský, CSc.
Department of Finance – Departments – University of Finance and Administration
Contact Person: Lenka Pokorná
Timetable of Seminar Groups
N_MaMF/cFPH: each odd Wednesday 12:15–12:59 S36, each odd Wednesday 13:00–13:45 S36, J. Brada
N_MaMF/pFPH: Wed 14:00–14:44 S36, Wed 14:45–15:30 S36, J. Brada
N_MaMF/vFPH: Fri 3. 11. 17:30–19:00 S24, 19:15–20:45 S24, Fri 24. 11. 17:30–19:00 S24, 19:15–20:45 S24, Sat 9. 12. 9:45–11:15 S24, 11:30–13:00 S24, P. Budinský
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, explain and actively used by: The models used in managing bond portfolios; The models used in managing equity portfolio; The models used in managing derivatives portfolio; The models used for forwards and swaps
Syllabus
  • 1. Statistical machinery I - Discrete and continuous random variables, the mean, variance and distribution function of a random variable.
  • 2. Statistical machinery II - Binomial distribution, normal distribution, the parameters of normal distribution, normal distribution quantiles and confidence intervals.
  • 3. Statistical machinery III - The sample mean and sample variance, sample covariance, sample correlation and correlation matrices.
  • 4. Bonds I - Bond Valuation and calculation of accrued interest income, the calculation of gross and net bond price, duration and convexity bond.
  • 5. Bonds II - Duration and convexity bond portfolio, static immunization due to interest rate risk. Comparison of portfolios with the same duration by convexity.
  • 6. Bonds III - Static and dynamic bond portfolio immunization (open and closed fund)
  • 7. Shares I - Valuation of shares. Market capitalization and its calculation, ratios based on share price.
  • 8. Shares II - Equity portfolio. Markowitz model, CAPM. The performance of the equity portfolio, Sharpe, Treynor and Jensen index)
  • 9. Derivatives I - Parameters affecting the price of futures contracts and options. Changes in the prices of options depending on these parameters.
  • 10. Derivatives II - Parameter Delta for call and put options. Interpretation of the parameter delta.
  • 11. Derivatives III - Delta immunization portfolio consisting of a call / put option and the underlying asset.
  • 12. Derivatives IV - Parity put-call options. Derivation of the put-call parity, the interpretation put-call parity, the influence of different parameters on option prices using the put-call parity.
Literature
    required literature
  • J. O. Grabbe: International Financial Markets, Elsevier Sc. Publ., 1986
  • P. Budinský, P. Záškodný: Finanční a investiční matematika, Praha 2004
    recommended literature
  • J. Hull: Options, Futures and Other Derivative Securities, Prentice-Hall 1993
  • P. Budinský, P. Záškodný: Ekonomická statistika, Praha 2004.
  • J. O. Grabbe: International Financial Markets, Elsevier Sc. Publ., 1986
  • D. Blake: Analýza finančních trhů, Grada Publ., Praha 1995
Teaching methods
eaching consists of lectures and exercises in full-time studies and controlled group consultations in the form of study. Minimum mandatory participation in exercises in full-time studies is 75%, the controlled group consultations in combined form 50%. Students who fail to meet the mandatory level of participation may be given during the semester additional study obligations (to the extent that will demonstrate academic achievement and acquired competencies necessary for successful completion of course).
Assessment methods
During one semester is required home work aimed at calculating the net price of the bond   details found on www.patria.cz; prerequisites: at least 80%-participation in the exercises and pass the written test - 10 closed questions a), b), c), d) - passed if at least 8 correctly test conditions: successful completion of the written - 4 examples (max 20 points) - to advance to the oral exam   must reach at least 10 points and then oral
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 2008, Winter 2009, Winter 2010, Winter 2011, summer 2012, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (Winter 2017, recent)
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