Faculty of Science and Mathematics / MATHEMATICS AND COMPUTER SCIENCE / FINANCIAL MATHEMATICS
| Course: | FINANCIAL MATHEMATICS/ |
| Course ID | Course status | Semester | ECTS credits | Lessons (Lessons+Exercises+Laboratory) |
| 5777 | Izborni | 1 | 6 | 2++0 |
| Programs | MATHEMATICS AND COMPUTER SCIENCE |
| Prerequisites | There is none |
| Aims | To acquire the basic concepts of financial mathematics and to be able to apply the theory in solving specific problems of financial mathematics. |
| Learning outcomes | Understanding of stock market functioning and the ability to implement mathematical models that describe stock market operations. |
| Lecturer / Teaching assistant | Darko Mitrovic |
| Methodology | Lectures, exercises, consultations, homework. |
| Plan and program of work | |
| Preparing week | Preparation and registration of the semester |
| I week lectures | Introduction to the subject. Multi period model. |
| I week exercises | Introduction to the subject. Multi period model. |
| II week lectures | Portfolio and trading strategy. |
| II week exercises | Portfolio and trading strategy. |
| III week lectures | Reachability and replication. Linear price functionals. |
| III week exercises | Reachability and replication. Linear price functionals. |
| IV week lectures | Non-arbitrage and functional strictly positive prices. |
| IV week exercises | Non-arbitrage and functional strictly positive prices. |
| V week lectures | Completeness and extensions. |
| V week exercises | Completeness and extensions. |
| VI week lectures | The first colloquium |
| VI week exercises | Solving the first colloquium |
| VII week lectures | Lectures - recapitulation of material. |
| VII week exercises | Exercises - recapitulation of the material |
| VIII week lectures | Martingales and asset pricing. |
| VIII week exercises | Martingales and asset pricing. |
| IX week lectures | The Fundamental Theorem on Asset Pricing. |
| IX week exercises | The Fundamental Theorem on Asset Pricing. |
| X week lectures | Cox-Ross-Rubinstein economics. |
| X week exercises | Cox-Ross-Rubinstein economics. |
| XI week lectures | Cox-Ross-Rubinstein model and its parameterization. |
| XI week exercises | Cox-Ross-Rubinstein model and its parameterization. |
| XII week lectures | Equivalent martingale measures, uniqueness and existence. |
| XII week exercises | Equivalent martingale measures, uniqueness and existence. |
| XIII week lectures | Prices and hedging in the Cox-Ross-Rubinstein model. |
| XIII week exercises | Prices and hedging in the Cox-Ross-Rubinstein model. |
| XIV week lectures | Second colloquium. |
| XIV week exercises | Solving the second colloquium. |
| XV week lectures | European options model |
| XV week exercises | European options model |
| Student workload | Classes and final exam: 6 hours and 40 minutes. 16=106 hours and 40 minutes. Necessary preparations 2 6 hours and 40 min. =13 hours and 20 minutes. Total workload for the subject: 5 30=150 Overtime: 0-30 hours Load structure 106 hours and 40 minutes (teaching) + 13 hours and 20 minutes (preparation) + 30 hours (additional work) |
| Per week | Per semester |
| 6 credits x 40/30=8 hours and 0 minuts
2 sat(a) theoretical classes 0 sat(a) practical classes 0 excercises 6 hour(s) i 0 minuts of independent work, including consultations |
Classes and final exam:
8 hour(s) i 0 minuts x 16 =128 hour(s) i 0 minuts Necessary preparation before the beginning of the semester (administration, registration, certification): 8 hour(s) i 0 minuts x 2 =16 hour(s) i 0 minuts Total workload for the subject: 6 x 30=180 hour(s) Additional work for exam preparation in the preparing exam period, including taking the remedial exam from 0 to 30 hours (remaining time from the first two items to the total load for the item) 36 hour(s) i 0 minuts Workload structure: 128 hour(s) i 0 minuts (cources), 16 hour(s) i 0 minuts (preparation), 36 hour(s) i 0 minuts (additional work) |
| Student obligations | Students are required to attend classes and do colloquiums. |
| Consultations | Monday 14:00-16:00 |
| Literature | P. Medina, S. Merino. Mathematical Finance and Probability, Birkhauser, 2005. |
| Examination methods | The maximum number of points on each colloquium is 30, and on the final exam it is 40. The minimum number of points for the passing grade is 51. |
| Special remarks | None |
| Comment | None |
| Grade: | F | E | D | C | B | A |
| Number of points | less than 50 points | greater than or equal to 50 points and less than 60 points | greater than or equal to 60 points and less than 70 points | greater than or equal to 70 points and less than 80 points | greater than or equal to 80 points and less than 90 points | greater than or equal to 90 points |
