# Introduction to Mathematical Finance (MATH313) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Introduction to Mathematical Finance MATH313 3 0 0 3 6
Pre-requisite Course(s)
Math 136
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Problem Solving. The main aim of this course is to provide students with a solid grounding in compound interest theory and experience of its application to the analysis of complex financial transactions. The compound interest model is developed in detail, and is applied to mortgage and commercial loans, to consumer credit transactions, to the valuation of securities, and to the measurement of investment performance. The term structure of interest rates is also covered. Uncertainty about future interest rates is modeled by assuming that future interest rates are random variables. The students who succeeded in this course; calculate the interest rates and make present value analysis use the standard interest functions and notations to write equations of value for financial transactions evaluate whether a project would be profitable understand discounted cashflow analysis using basic annuities Understand the fundamentals of bonds Introduction to theory of interest: simple and compound interest, time value of money, rate of interest, rate of discount, nominal rates, effective rates, compound interest functions, generalized cash flow modelling, loans, present value analysis, accumulated profit, and internal rate of return for investment projects, annuities, perpetuities, meas

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Introduction to theory of interest: Simple and compound interest Book1-pp. 1-7
2 Time value of money, Nominal rates, effective rates, rate of discount 1.Kitap -s. 10-13
3 Force of interest Book 1-pp. 14-17
4 Cash flows and Present value analysis Book 1-pp. 18-25
5 The equation of value, yields, annuities Book 1-pp. 36-54
6 Loan Schedules Book 1-pp. 55-61
7 Annuities payable pthly Book 1-pp. 66-72
8 Net present values and yields Book 1-pp. 86-93
9 The comparison investment projects , bonds Book 1-pp. 107-114 Other Source: 223-236
10 Probability Book 2-pp. 1-31
11 Geometric Brownian motion Book 2-pp. 32-37
12 Stochastic interest rates Book 1-pp. 269-286
13 Arbitrage and forward contracts Book 2-pp.63-70
14 The term structure of interest rates Other source: 301-320
15 Problem solving and review
16 Final Exam

### Sources

Course Book 1. An Introduction to Mathematics of Finance, J. J. McCutcheon and W. Scott, 1986. 2. An elementary introduction to mathematical finance, Options and other topics, Sheldon M. Ross, Cambridge University Press, 2003. 3. Mathematics of Investment and Credit, Samuel A. Broverman, ACTEX, 2010.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 7
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 35
Toplam 6 92
 Percentage of Semester Work 65 35 100

### 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 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 6 30
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 10 10