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Financial modelling 1

Code: 92987
ECTS: 5.0
Lecturers in charge: doc. dr. sc. Vanja Wagner - Lectures
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
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:
  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
Prerequisit for:
Enrollment :
Passed : Financial markets
Passed : Stochastic processes
3. semester
Mandatory course - Regular study - Financial and Business Mathematics
Consultations schedule: