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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 2023
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English, Czech
Teaching methods:	full-time
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 :	{One course of advanced Theory of Probability}
Incompatibility :	NMFM535
Interchangeability :	NMFM535
Is incompatible with:	NMFM535, NMFP505
Is interchangeable with:	NMFM535, NFAP012, NMFP505

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

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.

Last update: T_KPMS (13.05.2014)

Aim of the course -

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.)

Last update: T_KPMS (11.05.2015)

Course completion requirements -

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

Last update: Večeř Jan, doc. RNDr., Ph.D. (06.03.2018)

Literature - Czech

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.

Last update: T_KPMS (11.05.2015)

Teaching methods -

Lecture+exercises.

Last update: T_KPMS (22.04.2014)

Requirements to the exam -

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

Last update: Večeř Jan, doc. RNDr., Ph.D. (06.03.2018)

Syllabus -

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.

Last update: T_KPMS (11.05.2015)

Entry requirements -

A calculus based course on probability.

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