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Course, academic year 2022/2023
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Financial Derivatives 2 - NMFP466
Title: Finanční deriváty 2
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Jiří Witzany, Ph.D.
RNDr. Jakub Černý, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Volitelné
M Mgr. PMSE > Volitelné
Classification: Mathematics > Financial and Insurance Math.
Incompatibility : NMFM532
Interchangeability : NMFM532
Is incompatible with: NMFM532
Is interchangeable with: NMFM532
Annotation -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)
Stochastic modeling of stock prices, exchange rates, and interest rates. Introduction to standard and non-standard methods. Risk-neutral pricing. Itô's lemma and the Black-Scholes formula. Risk management for derivatives trading (Delta, Gamma etc., Value at Risk). Numerical estimations of volatilities and correlations. Monte Carlo simulations - pricing of exotic options.
Aim of the course -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)

The goal of the course is to provide an introduction to practical and theoretical aspects of financial derivatives with minimal assumptions in the area of mathematical calculus, statistics, and probability theory.

Course completion requirements -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)

Project solution, midterm test, final test.

Literature -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)


Witzany, J.: Derivatives - Theory and Practice of Trading, Valuation, and Risk Management. Springer Texts in Business and Economics, ISBN 978-3-030-51750-2, 2020 p. 376.


Witzany, J.: Financial Derivatives - Valuation , Hedging and Risk Management, 2013, Oeconomica.

Hull, John C.: Options, Futures, and Other Derivatives, 2015, 9th edition, Pearson.

Paul Wilmott: Paul Wilmott on Quantitative Finance, 2006, Wiley.

Steven E. Shreve: Stochastic Calculus for Finance I,II, 2004-5,Springer.

Witzany, Jiří: Credit Risk Management: Pricing, Measurement, and Modeling. Springer, ISBN 978-3-319-49799-0, 2017, p. 256.

Dvořák, Petr.: Deriváty, 2006, Oeconomica.

Witzany, Jiří: International Financial Markets, 2007, Oeconomica.

Cipra, Tomáš: Matematika cenných papírů, 2013, Professional Publishing.

Teaching methods -
Last update: RNDr. Jitka Zichová, Dr. (25.05.2022)

Lecture, partially online.

Requirements to the exam -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)

The final grade is based on the total score from a project assignment, midterm and final test. The midterm test comprises from 4-5 computational problems and theoretical questions based on the topics covered in the course before the test. The final test will have 6-8 computational problems and theoretical questions. The weight of the final will be at least 50%. The midterm test can be excused and in this case the final score is calculated proportionately just based on the final test and the midterm test. The standard cutoffs for the grades 1,2,3 are 90%, 75%, and 60%, and can be modified by the lecturer. The final test can be exceptionally retaken if agreed with the lecturer.

Syllabus -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)

Introduction to standard and non-standard methods for stochastic modeling of financial processes. Risk-neutral pricing. Change of numeraire and the equivalent martingale measure. Applications on valuation of selected exotic derivatives. Interest rate modeling and valuation of interest rate derivatives. Calibration of models - numerical estimations of volatilities and correlations. Credit risk modeling and credit derivatives.

Entry requirements -
Last update: doc. RNDr. Martin Branda, Ph.D. (11.12.2020)

heory of probability (Bachelor’s degree level), foundations of financial mathematics (interest rates, discounting, yield curve, exchange rates) and financial markets (basic instruments).

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