Mathematical Models of Derivatives Markets
General data
Course ID: | 1000-135IP1 |
Erasmus code / ISCED: |
11.923
|
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
|
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 2023/24" (in progress)
Time span: | 2024-02-19 - 2024-06-16 |
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MO TU W WYK
CW
TH FR |
Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
Coordinators: | Jacek Jakubowski | |
Group instructors: | Jacek Jakubowski | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Examination
Lecture - Examination |
Copyright by University of Warsaw.