ECONOMICS | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
ECF2222 | Differential Equations and Introduction to Stochastic Process | Fall Spring |
3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Departmental Elective |
Course Level: | Bachelor’s Degree (First Cycle) |
Mode of Delivery: | Face to face |
Course Coordinator : | Prof. Dr. GAZANFER ÜNAL |
Course Lecturer(s): |
Assoc. Prof. KAAN İRFAN ÖĞÜT |
Recommended Optional Program Components: | None |
Course Objectives: | Pioneering work of Bachelier (1900) on quantitative finance has led to unification of stochastic processes and differential equations. This topic nowadays is known as stochastic differential equations. After six dormant decades Black and Scholes (1976) have revived this approach by developing option pricing equation. This was the genesis of the financial engineering. Itô formula is central to Black and Scholes method. This led Itô to be cited more than Newton. Therefore, topic of this course is of paramount importance to finance and insurance. 1) Applications of probability theory to finance 2)Friendly introduction to stochastic processes 3)Introduction to Itô calculus 4)Derivation of Black and Scholes equation. |
The students who have succeeded in this course; 1.understand the importance of probability in finance 2.Cope with stochastic processes 3.Familiarity with Itô calculus 4. Understand the role of stochastic models |
Each topic mentioned above deserves to be taught seperately as an individual course. Therefore, course content would be a unique blend of probability theory, stochactic processes, Itô calculus, differential equations and stochastic models. The course will be delivered in such a way that suits the needs of the current students. Topic of the course are indeed required by many professional quantitative finance degrees. This alone pinpoints the urgence of this course to be delivered in the undergraduate program. |
Week | Subject | Related Preparation |
1) | Applications of probability in Finance | |
2) | Applications of probability in Finance | |
3) | Olasılık teorisinin finansal uygulaması | |
4) | Stochastic processes, Gaussianian processes | |
5) | Winer processes | |
6) | Itô formula | |
7) | Midterm | |
8) | Itô calculus | |
9) | Itô calculus | |
10) | Linear stochastic models | |
11) | Black and Scholes models | |
12) | Interest rate stochastic models | |
13) | Fokker-Planck equation | |
14) | Feynman-Kac method |
Course Notes / Textbooks: | Course Textbooks : 1)Ovidiu Calin (2015). An Informal Introduction to Stochastic Calculus with Applications, World Scientific Publishing Co. Pte. Ltd. 2)Alison Etheridge (2002). A course in Financial Calculus. Cambridge. |
References: | None |
Semester Requirements | Number of Activities | Level of Contribution |
Quizzes | 1 | % 20 |
Midterms | 1 | % 40 |
Final | 1 | % 40 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 3 | 42 |
Midterms | 1 | 30 | 30 |
Final | 1 | 35 | 35 |
Total Workload | 149 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | As a world citizen, she is aware of global economic, political, social and ecological developments and trends. | |
2) | He/she is equipped to closely follow the technological progress required by global and local dynamics and to continue learning. | |
3) | Absorbs basic economic principles and analysis methods and uses them to evaluate daily events. | |
4) | Uses quantitative and statistical tools to identify economic problems, analyze them, and share their findings with relevant stakeholders. | |
5) | Understands the decision-making stages of economic units under existing constraints and incentives, examines the interactions and possible future effects of these decisions. | |
6) | Comprehends new ways of doing business using digital technologies. and new market structures. | |
7) | Takes critical approach to economic and social problems and develops analytical solutions. | |
8) | Has the necessary mathematical equipment to produce analytical solutions and use quantitative research methods. | |
9) | In the works he/she contributes, observes individual and social welfare together and with an ethical perspective. | |
10) | Deals with economic problems with an interdisciplinary approach and seeks solutions by making use of different disciplines. | |
11) | Generates original and innovative ideas in the works she/he contributes as part of a team. |