In order to pass the course (grade 3) the student should be able to
construct models for pricing of financial derivatives;
price simple financial derivatives with risk neutral valuation;
present financial models and pricing to various users of financial instruments;
use stochastic calculus in various areas of application;
give an account of Feyman-Kac's representation formula and be able to use it to find solutions of parabolic partial differential equations.
Diffusion processes, stochastic integration and Ito's formula. Arbitrage theory in continuous time. Black-Scholes equation for pricing of financial instruments. Feynman-Kac's representation formula. Risk neutral valuation and hedging. Complete and incomplete markets. Applications to financial instruments such as options, forwards, futures, swaps, interest rate and currency derivatives.
Lectures and problem solving sessions.
Written examination and assignments.
The course can not be included in higher education qualification together with Financial mathematics II or the equivalent.