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
MAT5026 Stochastic Calculations 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.

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 stochastic processes arised in financial applications.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course:
◦will be able to define approximate stochastic process models and analyze them for a given research problem.
◦will be able to provide logical proofs of important theoretical results.
◦will be able to apply the theory of stochastic processes to model real random phenomena.
◦will be able to analyse financial stochastic processes.
◦will be able to model real life financial stochastic processes.

Course Content

The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Stochastic Processes: Definition and Classification
2) Risk processes
3) Poisson and Renewal Processes
4) Random Walk and Markov Chains (Discrete and Continuous times)
5) Martigale and Brownian Motion
6) Black-Scholes Option Pricing Model
7) Girsanov Theorem for the change of measure arguments
8) Risk Neutral Pricing and Currency Options with Partial Differential Equations
9) Pricing and Fixed Income Models
10) Jump processes and Option Pricing
11) Dynamic Arbitrage Pricing Theory
12) Simulation of Dynamic Econometric Models for Asset Returns
13) Asymptotic Theory for Estimation of Dynamic Econometric Models
14) Review

Sources

Course Notes / Textbooks: "Stochastic Processes for Insurance and Finance" by Tomasz Rolski, Hanspeter Schmidli, Volker Schmidt, and Jozef Teugels, John Wiley & Sons, 2009
References: "Stochastic Processes" by Sheldon Ross, Wiley Series in Probability and Mathematical Statistics.
"An Introduction to Stochastic Modeling" by S. Karlin and H.E. Taylor.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 3 % 15
Midterms 2 % 45
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.