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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 co-requisites: Math 111
Professional practice: No
Purpose of the course: Introduce the following concepts: Stochastic Differential Equations, Ito Calculus, Black-Scholes Partial Differential Equation, Pricing Financial Derivatives.
   Learning outcomes Up

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

  1. Model stochastic process,

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Using technology as an efficient tool to understand mathematics and apply it.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Solve Black-Scholes Partial Differential Equations

    Contribution to Program Outcomes

    1. 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.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
  3. Price Derivative Securities.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
   Contents Up
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, Risk-Neutral 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 Black-Scholes Partial Differential Equations.
Week 12: Solutions of Black-Scholes 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 7 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 15 1
Mid-term: 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)
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