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Mathematical Models of Derivatives Markets

General data

Course ID:	1000-135IP1
Erasmus code / ISCED:	11.923 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0619) Information and Communication Technologies (ICTs), not elsewhere classified The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Mathematical Models of Derivatives Markets
Name in Polish:	Modele matematyczne rynku instrumentów pochodnych I
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty 4EU+ (z oferty jednostek dydaktycznych) (in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective courses
Prerequisites:	Probability theory II 1000-115aRP2a
Prerequisites (description):	The student should have approved Probability Theory II. Knowledge of martingale theory in discrete time is essential. Introduction to Stochastic Analysis is recommended.
Short description:	During this course we describe and solve problems related to the modelling of financial markets and to the pricing and hedging of financial derivatives.
Full description:	Description of financial market, options, forward and futures contract, portfolio, arbitrage, replication, valuation. The finite market (discrete time market). Self-financing portfolio, contingent claims, arbitrage, replication, valuation. Martingale pricing. Completeness. The fundamental theorems. American options. Binomial model. Incomplete markets. Futures. Continuous time market. Black-Scholes model. Pricing of contingent claims, forward, futures contracts and exotic options.
Bibliography:	S. Pliska Introduction to mathematical finance: Discrete time models, 1997. Elliot, J.R., Kopp, P.E., Mathematics of Financial Markets, Springer-Verlag, New York 1999. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer-Verlag, 1997. SE Shreve Stochastic calculus for finance I: the binomial asset pricing model, 2005. SE Shreve Stochastic calculus for finance II: Continuous-time models, 2004. JM Steele, Stochastic calculus and financial applications, Springer 2012.
Learning outcomes:	Student - knows the basics of stochastic modeling of financial markets - knows the basic theorems of financial mathematics allowing to investigate the existence of arbitrage and the completeness of the market - knows various methods of valuation of derivatives - knows the methods of valuation of basic derivative instruments on the Blacka-Scholesa market
Assessment methods and assessment criteria:	The assessment criteria are specified in the description of the cycle.

Classes in period "Summer semester 2024/25" (past)

Time span:	2025-02-17 - 2025-06-08	Selected timetable range: weekly course term Go to timetable MO TU W WYK CW TH FR
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Jacek Jakubowski, Maciej Wiśniewolski
Group instructors:	Jacek Jakubowski
Students list:	(inaccessible to you)
Credit:	Course - Examination Lecture - Examination

Classes in period "Summer semester 2025/26" (future)

Time span:	2026-02-16 - 2026-06-07	Selected timetable range: weekly course term Go to timetable
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Jacek Jakubowski
Group instructors:	Jacek Jakubowski
Students list:	(inaccessible to you)
Credit:	Course - Examination Lecture - Examination

Course descriptions are protected by copyright.
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