Financial Calculus

Course Code:

AFN 406

Course Type:

Area Elective

P:

3

Application:

0

Credits:

3

ECTS:

6

Prerequisite Courses:

Advanced Mathematics

Principles of Finance

Course Language:

İngilizce

Course Objectives:

The purpose of the course is to provide students necessary skills to understand and interpret the mathematical models used in financial analysis, and apply these models to real-world financial problems.

Course Content:

Probability theory; random variables; Brownian motion; interest rate models ; Black-Scholes model; arbitrage pricing theory; time series models

Course Methodology:

1: Lecture, 2: Question-Answer, 3: Discussion, 4: Simulation, 5: Case Study

Course Evaluation Methods:

A: Testing, B: Presentation, C: Homework, D: Project, E: Laboratory

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1. To be able to use appropriate tools and techniques to analyze and interpret stock markets	4	1,2,3,4	A,B
2. To be able to critically analyze current problems in the fields of probability and stochastic processes, stochastic analysis and financial mathematics.	7,8	1,2,3,4	A,B
3. To be able to describe and formulate quantitative models for the purpose of modeling specific financial questions.	7,8	1,2,3,4	A,B
4. To be able to explain the basic notions and concepts behind the theory of pricing the financial instruments.	7,8	1,2,3,4	A,B

Course Flow

Week	Topics	Study Materials
1	Probability review	Textbook
2	Normal random variables	Textbook
3	Brownian motion and Geometric Brownian motion	Textbook
4	Interest rates: deterministic versus stochastic	Textbook
5	Pricing contracts via arbitrage	Textbook
6	Arbitrage theorem	Textbook
7	Black Scholes formula	Textbook
8	Portfolio selection	Textbook
9	Exotic options	Textbook
10	AR(p) (Auto Regressive) models and their statistical properties	Textbook
11	MA(q) (Moving Average) models and their statistical properties	Textbook
12	ARMA(p,q) (AutoRegressiveMoving Average) models and their statistical properties	Textbook
13	Assesment of probabilistic methods	Textbook
14	Review	Textbook

Recommended Sources

Textbook

Sheldon Ross, Mathematical Finance: Options and other topics 3rd ed. Cambridge (2011)

Additional Resources

Rosenkrantz Walter, A Introduction to probability and statistics for science, engineering, and finance

Material Sharing

Documents	Textbook, and lecture notes
Assignments	Homework
Exams	Mid-term and final exams

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	30
Quizzes	2	20
Assignment	1	50
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program


COURSE'S CONTRIBUTION TO PROGRAM
Program Learning Outcomes	Contribution
	1	2	3	4	5
1. To understand the core principles of finance and to be able to apply them both nationally and internationally.					X
2. To formulate solutions to finance problems by effectively using contemporary information technologies and up-to-date financial instruments.					X
3. To judge the best possible outcome to problems that require ethical and social responsibility-based thinking by identifying stakeholders and weighing alternative solutions.	X
4. To develop the necessary background to be able to work in multicultural and multilingual environments.				X
5. To analyze the developments in financial markets by interpreting and distinguishing among the factors affecting them.				X
6. To recognize management tools and models specific to multinational companies and to be able to apply them where necessary.				X
7. To understand the structure of the global economic system and to be able to analyze how new developments will affect this structure.				X
8. To be able to use critical thinking ability in decision making process.					X
9. To develop and demonstrate the leadership, teamwork and communication skills that may be transferred to the lifelong learning process.
10. To interpret environmental and sustainability issues by implementing quality management processes.				X

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Including the exam week: 16x Total course hours)	15	3	45
Hours for off-the-classroom study (Pre-study, practice)	15	3	45
Mid-terms	1	10	10
Homework	8	4	32
Final examination	1	15	15
Total Work Load			147
Total Work Load / 25 (h)			5.88
ECTS Credit of the Course			6

None

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