# 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)
Math 136
Course Language English Elective Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Drill and Practice. 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. The students who succeeded in this course; understand the modern mathematical concepts and methods in finance learn the stochastic techniques employed in derivative pricing calculate the European option prices using both the binomial model and the Black Scholes formula understand the early exercise futures of American options, put-call parity inequality and calculate the price of these options using binomial model learn the basic properties of Exotic options and interest rate models 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. 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

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 45 100

### Course Category

Core Courses X

### 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 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 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
4 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
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 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
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. 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

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