MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5027 | Calculation Modules in Finance | Fall | 3 | 0 | 3 | 12 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Dr. GENCO FAS |
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: | 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 |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 3 | % 15 |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 30 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
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 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 5 | 70 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 1 | 10 | 10 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 3 | 6 | 18 |
Preliminary Jury | 0 | ||
Midterms | 2 | 20 | 40 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 20 | 20 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |