ECONOMICS
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	Fall	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)	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.