SubjectsSubjects(version: 861)
Course, academic year 2019/2020
Stochastic Models for Finance and Insurance - NMFM505
Title: Stochastické modely pro finance a pojišťovnictví
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Večeř, Ph.D.
Class: M Mgr. FPM
M Mgr. FPM > Povinné
Classification: Mathematics > Financial and Insurance Math., Probability and Statistics
Pre-requisite : NMFM408
Annotation -
Last update: T_KPMS (13.05.2014)
Students are supposed to be acquainted with basics of probability theory and stochastic analysis on the level of Lecture NMFM 408 (or a similar lecture). In the present lecture the knowledge of basic tools of stochastic analysis will be extended, taking into account the usual tools used in continuous modelling in finance mathematics - e.g. the Ito formula, Girsanov Theorem and Representation Theorems for continuous martingales. Applications to interest rate models, risk neutral measures and option pricing. Arbitrage. Fundamental Theorem of Asset Pricing. Black-Scholes model. Hedging.
Aim of the course -
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.)

Course completion requirements -
Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)

Class attendance during the semester, the last class being mandatory.

Literature - Czech
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.

Teaching methods -
Last update: T_KPMS (22.04.2014)


Requirements to the exam -
Last update: doc. RNDr. Jan Večeř, Ph.D. (06.03.2018)

A written final exam covering the topics listed in the syllabus.

Syllabus -
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.

Entry requirements -
Last update: RNDr. Jitka Zichová, Dr. (17.06.2019)

A calculus based course on probability.

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