M5123 Mathematics of Finance

Faculty of Science
Autumn 2023
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. Silvie Zlatošová, Ph.D. (lecturer)
Guaranteed by
Mgr. Silvie Zlatošová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M5123/01: Wed 10:00–10:50 M6,01011, S. Zlatošová
Prerequisites
M1100 Mathematical Analysis I || M2510 Mathematical Analysis 2 || M1101 Mathematical Analysis I || M1100F Mathematical Analysis I
Calculus, probability theory
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This is an introductory course in mathematical modelling in finance. It covers mainly discrete models for pricing financial derivatives.
Learning outcomes
At the end of the course students should be able to: - set up discrete models for securities prices - use the risk-neutral probability measure - verify market completeness in a given model - formulate and use the fundamental theorem of arbitrage pricing
Syllabus
  • Basic concepts of probability theory
  • Introduction to financial derivatives
  • 1-period model with 2 scenarios, pricing of European options
  • General 1-period model, risk-neutral probability measure, replicating portfolio
  • Fundamental theorem of arbitrage pricing, complete and incomplete markets, put-call parity
  • Discrete model with several periods, binomial models
  • Hedging in binomial models
  • Bonds and the time structure of interest rates
  • Forward interest rates, bond duration
  • Bond duration and convexity, bond portfolio immunization
  • Application of the duality theorem of a system of linear equations to a bond portfolio, bonds with a floating coupon
  • Introduction to portfolio theory, Markowitz model
Literature
  • HULL, John. Options, futures, and other derivatives. Ninth, Global edition. Harlow, England: Pearson. 1 online. ISBN 9781292212920. 2018. URL info
  • MELICHERČÍK, Igor, Ladislava OLŠAROVÁ and Vladimír ÚRADNÍČEK. Kapitoly z finančnej matematiky. [Bratislava: Miroslav Mračko. 242 s. ISBN 8080576513. 2005. info
  • BAXTER, Martin and Andrew RENNIE. Financial calculus : an introduction to derivative pricing. New York, NY: Cambridge University Press. ix, 233. ISBN 0521552893. 1996. info
Teaching methods
Lectures, exercises, homeworks
Assessment methods
Two written tests during the semester, consisting of 5 problems each. 50% of total points is needed to pass. Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms autumn 2021, Autumn 2022.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/M5123