Invited Lecture - Abstract

This talk describes two types of paradigm problems in continuous time finance, one in the area of equity derivatives, the other in the area of interest rate derivatives. The way in which the underlying assets are modelled as stochastic processes is briefly described. The princple behind the pricing of derivative securities is explained (basically modern financial markets do not leave any free lunches hanging around) and shown to reduce, in a fairly general situation, to the solution of an intergro-partial differential equation subject to various types of boundary conditions. The way in which the pricing problem can also be transformed to one involving Monte-Carlo simulation is touched upon briefly. The essential differences between the pricing of equity and interest rate derivatives is explained. A number of ongoing computational problems in this area are outlined.