APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5027 Calculation Modules in Finance Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. GENCO FAS
Recommended Optional Program Components: None
Course Objectives: This course aims to provide the definition and analysis of
scientific computation and simulation in finance. It is a crossdisciplinary field which relies on mathematical finance, numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course:
◦will be able to solve Linear and Non Linear Equations by using methods.
◦will be able to provide logical proofs of important theoretical results.
◦will be able to apply simulation tecniques to financial problems.
◦will be able to make financial decisions using numerical tecniques.

Course Content

The topics covered in this course include numerical methods and computer simulations to make trading, hedging and investment decisions, as well as facilitating the risk management of those decisions.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Errors, Condition Numbers, Norms
2) Solving Linear Systems (Application: Markov Chains)
3) Best fit and least squares (Application: CAPM)
4) Nonlinear Equations (Application: Implied Volatility)
5) Optimization (Application: Optimal Portfolios)
6) Interpolation (Application)
7) Quadrature (Application: Pricing European Claims)
8) Numerical MEthods for ODEs
9) Black-Scholes PDE and Heat Equation
10) Explicit Finite Differences for PDEs
11) Backward Finite Differences & Crank-Nicolson Scheme
12) Pricing European Claims
13) CRR Model and Binomial trees
14) Numerical Methods for American Options

Sources

Course Notes / Textbooks: Seydel, R. "Tools for Computational Finance" (latest edition).
Siegman and Davis. "Matlab Primer", Chapman/Hall.
References: "Implementing derivative models" by L. Clewlow, Ch. Strickland. John Wiley and Sons, Ltd., 1998.
"Statistical Analysis of Financial Data in SPlus" by Ren A. Carmona. Springer Texts in Statistics, January 2004.
"Introduction to Stochastic Calculus Applied to Finance" by D. Lamberton and B. Lapeyre. Chapman and Hall/CRC, 1996.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 14 % 15
Quizzes 3 % 15
Midterms 2 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 5 70
Project 1 10 10
Quizzes 3 6 18
Midterms 2 20 40
Final 1 20 20
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.