This course focuses on the continuous-time modelling of financial market under deterministic interest rates. The main goal of the course is a detailed study of the classical Black-Scholes options pricing model and extensions. The notion of a continuously rebalanced trading strategy is introduced and the arbitrage-free and completeness properties of a financial market model are examined. We also introduce and study the concepts of historical, implied and stochastic volatilities. In the second part of the course, we study contingent claim of American style in the Black-Scholes set-up.

Pre-requisites: 24 units of level III mathematics or a degree in a numerate discipline or permission of the Head of Department.