Course: Financial mathematics 2

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Course title Financial mathematics 2
Course code KMA/FIM2
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Talašová Jana, doc. RNDr. CSc.
  • Bohanesová Eva, Mgr. Ph.D.
Course content
1. Bonds; bond price 2. Term structure of interest rates 3. Yield curves; bonds and arbitrage 4. Arbitrage portfolio; premature redemption 5. Duration of a bond 6. Immunization of a bond portfolio 7. Immunization of a bond portfolio - additional problems 8. Random interest rate; stochastic procesess, Brownian motion 9. Ito´s lemma; modeling of stock market price 10. Modeling of option price - binomial tree model 11. Change of the probability measure 12. Modeling of option price - continuous case

Learning activities and teaching methods
Lecture, Projection (static, dynamic)
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 40 hours per semester
Learning outcomes
To gain knowledge of selected parts of advanced mathematics of finance.
Learn to construct a yield curve, to analyze bonds on the base of arbitrage, on the risk of premature redemption and on the changes in interest rates; learn to use special instruments to model stock and option market price.

Assessment methods and criteria
Oral exam, Student performance

Credit: to have the demanded presence in the Exercises, to gain at least half of the max. number of points in the written test. Exam: to understand all the particular parts of the object, to be able to derive the corresponding formulae and relations.
Recommended literature
  • I. Melicherčík a kol. (2005). Kapitoly z finančnej matematiky 1. Zvolen.
  • M. Baxter, A. Rennie . (1996). Financial calculus, An introduction to derivatice pricing. Cambridge.
  • T. Cipra. (2000). Matematika cenných papírů. Praha.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses 1 Winter