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Last update: T_KPMS (13.05.2014)
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Last update: T_KPMS (11.05.2015)
The subject is aimed at advanced methods of stochastic analysis and fundamental models of finance mathematics where these methods are exploited (option pricing, hedging, etc.) |
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Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)
Class attendance during the semester, the last class being mandatory. |
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Last update: T_KPMS (11.05.2015)
S.E.Shreve: Stochastic Calculus for Finance II, Continuous Time Models, Springer-Verlag, 2004 I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer-Verlag, 1988 (první vydání) J. M. Steele, Stochastic Calculus and Financial Applications, Springer-Verlag, 2001 J. Seidler, Vybrané kapitoly ze stochastické analysy, Matfyzpress, 2011. |
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Last update: T_KPMS (22.04.2014)
Lecture+exercises. |
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Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)
A written final exam covering the topics listed in the syllabus. |
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Last update: T_KPMS (11.05.2015)
1. Stochastic integration w.r.t. martingales and local martingales. Stochastic linear and bilinear equations, geometric Brownian motion. Stochastic differential equations. 2. Short rates models (Ho and Lee, Vasicek, Hull and White, CIR) , bond price. 3. Market model, portfolio value, self-financing portfolio. Risk-neutral measures, arbitrage and the 1st fundamental theorem of option pricing. 4. Girsanov theorem and risk-neutral measure in the BS model. European call option. Completeness of the market, 2nd fundamental theorem of option pricing. 5. Representation of continuous martingale by stochastic integral, hedging. 6. Feynman-Kac formula, BS equation, replication strategy for simple contingent claims. Asian and American options. |
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Last update: RNDr. Jitka Zichová, Dr. (17.06.2019)
A calculus based course on probability. |