Load:
|
1. komponenta
Lecture type | Total |
Lectures |
45 |
* Load is given in academic hour (1 academic hour = 45 minutes)
|
Description:
|
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.
|
Literature:
|
- D. Lamberton, B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance
- M. Musiela, M. Rutkowski: Martingale Methods in Financial Modelling
- J. Cvitanić, F. Zapatero: Introduction to the Economics and Mathematics of Financial Markets
- S. R. Pliska: Introduction to Mathematical Finance: Discrete Time Models
- H. Föllmer, A. Schied: Stocahstic Finance: An Introduction in Discrete Time
- J. C. Hull: Options, Futures, and Other Derivative Securities, 5th edition
- S. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model
|
Prerequisit for:
|
Enrollment
:
Passed
:
Financial markets
Passed
:
Stochastic processes
|