APPLIED MATHEMATICS (TURKISH, NON-THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5027 | Calculation Modules in Finance | Fall Spring |
3 | 0 | 3 | 12 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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. |
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. |
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. |
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 |
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. |
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 |
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 |
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. |