FINANCIAL MATHEMATICS (96h)
Responsible lecturer: Jerzy Dzieża, PhD**
Lectures: 48 hours; laboratory: 48 hours;.

Lecture topics
1. Stochastic Processes in Discrete Time (lectures: 12 hours; laboratory: 12 hours)
Information and filtration
Definition and basic properties of martingales
Martingale transforms
Stopping times
The Snell envelope and optimal stopping

2. Discrete Models of Financial Markets (lectures: 12 hours; laboratory: 12 hours)
Single-step binomial tree: option pricing
Multi-step binomial model: Cox-Ross-Rubinstein model, delta hedging
Multi-step general models: conditional expectation, trading strategies and arbitrage, fundamental theorem of asset pricing,
American options: pricing, stopping times and optimal exercise

3. Stochastic Processes in Continuous Time (lectures: 12 hours; laboratory: 12 hours)
Brownian motion
Stochastic integrals
Ito calculus

4. The Black-Scholes Model (lectures: 12 hours; laboratory: 12 hours)
Risk neutral pricing
Pricing and hedging contingent claims
The Greeks
Examples of exotic options

**Jerzy Dzieża, PhD
Director of postgraduate studies in Financial Mathematics and Senior Lecturer at Applied Mathematics Department, AGH University of Science and Technology, Kraków, Poland. He published many papers and prepared teaching lectures on Fixed Income Securities, Derivative Securities, Real Options and Risk Management.
Since 1998 till 2005 he was a Scientific Editor of first Polish journal on derivatives ‘Rynek terminowy’ (Futures Market). He cooperated with Polish Stock Exchange (portfolio hedging project) and Polish Energy Exchange (risk management project) and few Polish companies on risk management projects.