Mathematical Models of Derivatives Markets 1000-135IP1
Description of financial market, options, forward and futures contract, portfolio, arbitrage, replication, valuation.
The finite market (discrete time market). Self-financing portfolio, contingent claims, arbitrage, replication, valuation. Martingale pricing. Completeness. The fundamental theorems. American options. Binomial model. Incomplete markets. Futures.
Continuous time market. Black-Scholes model. Pricing of contingent claims, forward, futures contracts and exotic options.
Type of course
Prerequisites
Prerequisites (description)
Course coordinators
Learning outcomes
Student
- knows the basics of stochastic modeling of financial markets
- knows the basic theorems of financial mathematics allowing to investigate the existence of arbitrage and the completeness of the market
- knows various methods of valuation of derivatives
- knows the methods of valuation of basic derivative instruments on the Blacka-Scholesa market
Assessment criteria
The assessment criteria are specified in the description of the cycle.
Bibliography
S. Pliska Introduction to mathematical finance: Discrete time models, 1997.
Elliot, J.R., Kopp, P.E., Mathematics of Financial Markets, Springer-Verlag, New York 1999.
Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer-Verlag, 1997.
SE Shreve Stochastic calculus for finance I: the binomial asset pricing model, 2005.
SE Shreve Stochastic calculus for finance II: Continuous-time models, 2004.
JM Steele, Stochastic calculus and financial applications, Springer 2012.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Bachelor's degree, first cycle programme, Mathematics
- Master's degree, second cycle programme, Mathematics
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: