PřF:M5123 Mathematics of Finance - Course Information
M5123 Mathematics of Finance
Faculty of ScienceAutumn 2024
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching - 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 11:00–12:50 M3,01023
- Timetable of Seminar Groups:
- 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
- Mathematics (programme PřF, B-MA)
- 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, 2018, 1 online. ISBN 9781292212920. URL info
- MELICHERČÍK, Igor, Ladislava OLŠAROVÁ and Vladimír ÚRADNÍČEK. Kapitoly z finančnej matematiky. [Bratislava: Miroslav Mračko, 2005, 242 s. ISBN 8080576513. info
- BAXTER, Martin and Andrew RENNIE. Financial calculus : an introduction to derivative pricing. New York, NY: Cambridge University Press, 1996, ix, 233. ISBN 0521552893. 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
- The course is taught annually.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2024/M5123