Syllabus ( MATH 432 )

Basic information


Course title: 
Mathematics of Financial Derivatives 
Course code: 
MATH 432 
Lecturer: 
Prof. Dr. Oğul ESEN

ECTS credits: 
6 
GTU credits: 
3 () 
Year, Semester: 
4, Fall and Spring 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Departmental Elective

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
Math 111 
Professional practice: 
No 
Purpose of the course: 
Introduce the following concepts: Stochastic Differential Equations, Ito Calculus, BlackScholes Partial Differential Equation, Pricing Financial Derivatives. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Model stochastic process,
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Using technology as an efficient tool to understand mathematics and apply it.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Solve BlackScholes Partial Differential Equations
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Written exam

Price Derivative Securities.
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Written exam


Contents


Week 1: 
Mathematical Prelude: Stochastic Differential Equations, Partial Differential Equations. 
Week 2: 
Financial Prelude: A Toy Model. 
Week 3: 
Time Value of Money, Bounds. 
Week 4: 
Expected Return, Binomial Tree Model, RiskNeutral Probability, Martingale Property. 
Week 5: 
The Principle of No Arbitrage, Discrete Models. 
Week 6: 
Forward and Futures Contracts 
Week 7: 
Midterm Exam and Solutions of Some Problems 
Week 8: 
Continuous Probability: A further Analysis of Expectation and Variance 
Week 9: 
Introduction to Options 
Week 10: 
From Random Walk to Wiener Process, Stochastic Differential Equations 
Week 11: 
Ito Lemma, Derivation of BlackScholes Partial Differential Equations. 
Week 12: 
Solutions of BlackScholes Partial Differential Equations. 
Week 13: 
Options Pricing via Risk Neutral Measure 
Week 14: 
Sensitivity analysis and Greeks 
Week 15*: 
 
Week 16*: 
Final Exam 
Textbooks and materials: 
[B] J.R. Buchanan, (2006), An undergraduate Introduction to Financial Mathematics, World Scientific. [S] W.A. Strauss, (2008), Partial Differential Equations, An Introduction, 2nd Edition, John Wiley and Sons. 
Recommended readings: 
[CZ] M. Capinski and T. Zastawniak, (2003) Mathematics for Finance: An Introduction to Financial Engineering, Springer. 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
7 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
0 
0 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
15 
1 

Midterm: 
2 
1 

Personal studies for final exam: 
30 
1 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



>