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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.
Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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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. Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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Project solution, midterm test, final test. Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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Required:
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.
Optional:
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. Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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Lecture, partially online. Last update: Zichová Jitka, RNDr., Dr. (25.05.2022)
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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. Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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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. Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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heory of probability (Bachelor’s degree level), foundations of financial mathematics (interest rates, discounting, yield curve, exchange rates) and financial markets (basic instruments). Last update: Branda Martin, doc. RNDr., Ph.D. (11.12.2020)
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