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.

Course coordinators

Urszula Kuta

Type of course

elective courses

Prerequisites

Probability theory II

Prerequisites (description)

The student should have approved Probability Theory II. Knowledge of martingale theory in discrete time is essential. Introduction to Stochastic Analysis is recommended.

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.