1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To explain financial market models in discrete time and introduce probabilistic tools for precise mathematical description and understanding of these models.

COURSE DESCRIPTION AND SYLLABUS:
1. One period models. Model description: financial assets, portfolios, arbitrage. Arbitrage free models and martingale measure; fundamental theorem. Derivatives; arbitrage free prices; replicating portfolio. Complete market models. Return and risk.
2. Dynamic discrete models.: Model description: financial assets, dynamic portfolios, arbitrage. Martingales. Arbitrage free models and martingale measure; fundamental theorem. Derivatives; arbitrage free prices; replicating portfolio. Complete market models. Introduction in american options. The Cox - Ross - Rubinsteinov model.
3. Optimal stopping problem and american options. Stopping times. The Snell envelope. Decomposition of a supermartingale. The Snell envelope and Markov chains. Applications to american options in the CRR model.

1. D. Lamberton, B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance
2. M. Musiela, M. Rutkowski: Martingale Methods in Financial Modelling
3. J. Cvitanić, F. Zapatero: Introduction to the Economics and Mathematics of Financial Markets
4. S. R. Pliska: Introduction to Mathematical Finance: Discrete Time Models
5. H. Föllmer, A. Schied: Stocahstic Finance: An Introduction in Discrete Time
6. J. C. Hull: Options, Futures, and Other Derivative Securities, 5th edition
7. S. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model

Enrollment :
Passed : Financial markets
Passed : Stochastic processes

Mandatory course - Regular study - Financial and Business Mathematics