The aim of the course is to provide students with the ability to understand mathematical models used in financial analysis and to apply them in solving real-life financial problems.
From Random Motion to Brownian Motion, quadratic variations and volatility, stochastic integrals, martingale property, Ito formula, Geometric Brownian Motion, solution of Black-Scholes equation, stochastic differential equations, Feynman-Kac Theorem, Cox-Ingersoll-Ross and Vasicek Models, Girsanov Theorem and risk-free measurements, Heath-Jarrow-Morton Model, currency exchange instruments.
Vertical Tabs
Course Learning Outcomes
|
Course Learning Outcomes |
Program Learning Outcomes |
Teaching Methods |
Assessment Methods |
|
Study of stochastic processes |
|
1,2,3 |
A,B,C,D |
|
Applications of the Ito integral for stochastic analysis and Wiener and Poisson processes |
|
1,2,3 |
A,B,C,D |
|
Solution of stochastic differential equations for Wiener process and finance applications of CIR, MOU and BUX models |
|
1,2,3 |
A,B,C,D |
|
Girsanov theorem, Fokker-Planck equations and their applications in finance |
|
1,2,3 |
A,B,C,D |
|
Feynman-Kac theorem and its applications in finance |
|
1,2,3 |
A,B,C,D |
Course Flow
| COURSE CONTENT | ||
| Week | Topics | Study Material |
| 1 | Introduction | |
| 2 | Probability Theory | |
| 3 | Markov and Chebyshev inequalities, Central Limit Theorem | |
| 4 | Gaussian processes | |
| 5 | Wiener processes, Kolmogorov continuity criterion | |
| 6 | Poisson process, Telegraph process, Unified Poisson process | |
| 7 | Wiener-Ito integral, Ito lemma for Wiener and Poisson processes | |
| 8 | Ito isometries, Poisson integral, Martingale and Semi-Martingale | |
| 9 | Midterm | |
| 10 | Stochastic differential equations for the Wiener process | |
| 11 | CIR, MOU and BUX models in finance | |
| 12 | Girsanov theorem, Fokker-Planck equations and their applications in finance | |
| 13 | Feynman-Kac theorem and its applications in finance | |
| 14 | Stochastic differential equations for the Jump process | |
| 15 | Merton's model | |
| 16 | Final | |
Recommended Sources
| RESOURCES | |
| Course Note | G. Ünal : Lecture Notes |
| Other Resources |
M. Baxter and A.Rennie, Financial Calculus, CUP (2003).
A.G. Malliaris, Stochastic Methods in Economics and Finance, Elsevier (1999). S. Neftçi, An introduction to Financial derivatives AP 2nd ed. S.E. Shreve, Stochastic calculus for Finance Vol 1 and 2 Springer (2004) B. Oksendal, Introduction to stochastic differential equations 5th edition 2003 Springer ,L. C. Evans, An Introduction to stochastic differential equations Berkeley Lecture Notes 2005. |
Assessment
| ASSESSMENT | ||
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-Term | 1 | 60 |
| Project | ||
| Homework | 10 | 40 |
| Final Exam | 1 | 100 |
| Total | 100 | |
|
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE |
50 | |
|
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE |
50 | |
| Total | 100 | |
Course’s Contribution to Program
| COURSE'S CONTRIBUTION TO PROGRAMME | ||||||
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Students can keep themselves informed and analyze the current economic development in Turkey and in the world from an international political economy perspective paying a particular attention to the interaction of the Turkish economy with the global economy. | X | ||||
| 2 | Being aware of the development and accumulation of economic thought, students can master qualitative and quantitative knowledge and methods to test various economic theories that can be applied to the analysis of the current economic problems. | X | ||||
| 3 | Students can use statistical and econometric analyses by learning how to use information technologies that have validity and widespread use in the field of economics. | X | ||||
| 4 | By learning how to learn in the field of economics, students can research and work individually or as a team using the Turkish and English academic resources. | X | ||||
| 5 | Being aware of the ethical values, students know the individual, social and ecological dimensions of the concept of social responsibility and can prove that they understand the active citizenship duty that falls upon them within this framework. | X | ||||
| 6 | Students can clearly express, present and share their knowledge, the outcomes of their studies, their ideas and comments to people in their field or other disciplines/units using the necessary data, in national and international academic and professional environments, in Turkish or English. | X | ||||
ECTS
| ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION | ||||
| Activities | Quantity | Duration (Hour) | Total Workload (Hour) | |
|
Course Duration (Including the exam week: 15x Total course hours/week) |
16 | 3 | 48 | |
|
Hours for off-the-classroom study (Pre-study, practice, review/week) |
16 | 5 | 80 | |
| Homework | 10 | 6 | 60 | |
| Mid-term | 1 | 20 | 20 | |
| Final | 1 | 40 | 40 | |
| Total Work Load | 248 | |||
| Total Work Load / 25 (h) | 9.92 | |||
| ECTS Credit of the Course | 10 | |||