ECTS - Mathematics of Financial Derivatives
Mathematics of Financial Derivatives (MATH316) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics of Financial Derivatives | MATH316 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH136 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Drill and Practice. |
| Course Lecturer(s) |
|
| Course Objectives | Mathematical modelling of finance is a new area of application of mathematics; it is expanding rapidly and has great importance for world financial markets. The course is concerned with the valuation of financial instruments known as derivatives. The course aims to enable students to acquire active knowledge and understanding of some basic concepts in financial mathematics including stochastic models for stocks and pricing of financial derivatives. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Introduction to options and markets, European call and put options, arbitrage, put call parity, asset price random walks, Brownian motion, Ito?s Lemma, derivation of Black-Scholes formula for European options, Greeks, options for dividend paying assets, multi-step binomial models, American call and put options, early exercise on calls and puts on a |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Introduction to Options and Markets, Probability | pp. 1-13 Other source 2: pp. 1-25 |
| 2 | Brownian motion (Weiner Process), Geometric Brownian Motion | Other source 2: pp. 26-35 |
| 3 | Asset price random walks, Ito’s Lemma | pp. 18-30 |
| 4 | One step and multi-step binomial model for option pricing | pp. 180-187 |
| 5 | European call and put options. Payoffs and strategies, No arbitrage principle | pp. 33-40 |
| 6 | Black-Scholes equation, Final and boundary conditions | pp. 41-48 |
| 7 | Problem solving and review | |
| 8 | Midterm | |
| 9 | Greeks, Hedging | pp. 51-52 |
| 10 | Options for dividend payoff assets | pp. 90-97 |
| 11 | American call and put options, early exercise on calls and puts on a non-dividend-paying stocks | pp. 106-108 |
| 12 | American options as the free boundary value problems | pp. 109-120 |
| 13 | Exotic options | pp. 195-209 |
| 14 | Interest rate models. | pp. 263-268 |
| 15 | Problem solving and review | |
| 16 | Final Exam |
Sources
| Course Book | 1. The Mathematics of Financial Derivatives: A student introduction, P. Wilmott,S. Howison and J. Dewynne, Cambridge University Press, 1995. |
|---|---|
| Other Sources | 2. Options, Futures and Other Derivatives, J. Hull, Prentice Hall, 2006. |
| 3. . An Elementary Introduction to Mathematical Finance. Options and Other Topics. (Second Edition), by Sheldon M. Ross, Cambridge University Press, 2003, | |
| 4. An Introduction to the Mathematics of Financial Derivatives, by Salih N. Neftci, Academic Press, 2000. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 35 |
| Final Exam/Final Jury | 1 | 45 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 55 |
|---|---|
| Percentage of Final Work | 45 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 10 | 50 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 16 | 16 |
| Prepration of Final Exams/Final Jury | 1 | 22 | 22 |
| Total Workload | 130 | ||