# Computational Methods of Mathematical Finance (MATH417) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Computational Methods of Mathematical Finance MATH417 Area Elective 2 0 2 3 6
Pre-requisite Course(s)
Math 316
Course Language English Elective Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Problem Solving. The goal of the course is to introduce the students to numerical methods in finance and option theory. The students who succeeded in this course; learn the finite difference methods for valuation of European options understand the numerical methods for American options know the methods for random number generation understand option pricing by Monte Carlo simulation Introduction to MATLAB, finite difference formulae, the explicit and implicit finite difference methods, The Crank-Nicolson method, European option pricing by the heat equation, pricing by the Black-Scholes equation, pricing by an explicit, an implicit and Crank-Nicolson method, pricing American options, projected SOR and tree methods, pseudo-rando

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Introduction to MATLAB pp. 263-286
2 Finite difference formulae pp. 195-199
3 The explicit finite difference method pp. 203-214
4 The fully implicit method pp. 215-219
5 The Crank-Nicolson method pp. 220-225
6 European option pricing by the heat equation pp. 226-233
7 Problem solving and review
8 Midterm Exam
9 Pricing by the Black-Scholes equation pp. 234-244
10 Pricing American options, Projected SOR and tree methods pp. 245-262
11 Pseudo-Random numbers, Inverse transform method pp. 140-148
12 Acceptance-Rejection and Box-Muller methods, The polar method of Marsaglia pp. 149-155
13 Monte Carlo integration pp. 160-165
14 Option pricing by Monte Carlo simulation pp. 166-178
15 Problem solving and review
16 Final Exam

### Sources

Course Book 1. An Introduction to Computational Finance, Ö. Uğur, Imperial College Press, 2009. 2. Options, Futures and Other Derivatives, J. Hull, Prentice Hall, 2006. 3. The Mathematics of Financial Derivatives: A student introduction, P. Wilmott,S. Howison and J. Dewynne, Cambridge University Press, 1995.

### 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) 16 2 32
Laboratory 16 2 32
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 8 40
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 12 12
Prepration of Final Exams/Final Jury 1 20 20