BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| ECONOMICS AND FINANCE | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| ECF2222 | Differential Equations and Introduction to Stochastic Process | Spring | 3 | 0 | 3 | 6 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| 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. |
Learning Outcomes
|
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 |
Course Content
| 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. |
Weekly Detailed Course Contents
| 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 |
Sources
| 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 |
Evaluation System
| 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 | |
ECTS / Workload Table
| 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 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Build up a body of knowledge in mathematics and statistics, to use them, to understand how the mechanism of economy –both at micro and macro levels – works. | 4 |
| 2) | Understand the common as well as distinctive characters of the markets, industries, market regulations and policies. | 4 |
| 3) | Develop an awareness of different approaches to the economic events and why and how those approaches have been formed through the Economic History and understand the differences among those approaches by noticing at what extent they could explain the economic events. | 4 |
| 4) | Analyze the interventions of politics to the economics and vice versa. | 3 |
| 5) | Apply the economic analysis to everyday economic problems and evaluate the policy proposals for those problems by comparing opposite approaches. | 4 |
| 6) | Understand current and new economic events and how the new approaches to the economics are formed and evaluating. | 5 |
| 7) | Develop the communicative skills in order to explain the specific economic issues/events written, spoken and graphical form. | 4 |
| 8) | Know how to formulate the economics problems and issues and define the solutions in a well-formed written form, which includes the hypothesis, literature, methodology and results / empirical evidence. | 4 |
| 9) | Demonstrate the quantitative and qualitative capabilities and provide evidence for the hypotheses and economic arguments. | 4 |
| 10) | Understand the information and changes related to the economy by using a foreign language and communicate with colleagues. | 4 |