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Mathematical models of option pricing

ДВС.3.08

Вибіркова дисципліна для ОП

First

2023/2024

8 Semester

4

PH03. Formalize the tasks formulated in the language of a particular subject area; formulate their mathematical formulation and choose a rational solution method; solve the obtained problems by analytical and numerical methods, evaluate the accuracy and reliability of the obtained results. PH13. Use in practice specialized software products and software systems for computer mathematics. PRN22.3. Know the main sections of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics;

Full-time form

To successfully study the discipline "Mathematical models of option pricing" the student must meet the following requirements: Know: 1. fundamental bases of mathematical methods of construction, verification, research of qualitative characteristics of deterministic and stochastic mathematical models. 2. classical methods of mathematical analysis, probability theory, operations research. Be able to: 1. to study the qualitative characteristics of the constructed mathematical models. 2. formulate mathematical optimization problems for such models. 3. apply classical methods for the study of applied problems in deterministic and stochastic models. Possess: 1. skills of using classical methods of mathematical analysis and probability theory. 2. skills of search and analysis of information in open sources.

The course is aimed at mastering the basic theoretical principles that underlie the modeling of financial markets, principles, and methods of solving problems related to minimizing market risks and mastering practical skills in solving hedging problems and determining the option price.

1. Bean Michael A., Probability: The science of uncertainty, AMS:Providence, 2009. 2. Paul W., Baschangel J., Stochastic Processes: From Physics to Finance, Springer, 1999. 3. Husak D.V., Kulik A.M., Pylypenko A.A., Mishura YU.V., Zbirnyk zadach z finansovoyi matematyky ta teoriyi ryzyku, Kyyiv, 2008r.

Lectures, consultations, test works, independent work.

Semester assessment: Maximum number of points that can be obtained by a student: 60 points: 1. Test work №1: PH 1.1, PH 2.1, PH 2.2, PH 2.3 - 30/18 points. 2. Test work № 2: PH 2.4, PH 3.1, PH 3.2, PH 4.1, PH 4.2 - 30/18 points. Final assessment (in the form of an exam): Maximum number of points that can be obtained by a student: 40 points. Learning outcomes to be evaluated: PH 1.1, PH 2.1, PH 2.2, PH 2.3, PH 2.4, PH 3.1, PH 3.2, PH 4.1, PH 4.2. Form of conducting: written. Types of tasks: 4 written tasks (2 theoretical questions and 2 practical tasks). A student receives an overall positive grade in the discipline if his grade for the exam is not less than 24 (twenty four) points. A student is admitted to the exam if during the semester he: scored at least 36 points; performed and timely submitted at least 2 (two) independent works from the list of proposed works;

Ukrainian