This talk was given by Istvan Redl on the 8 October 2013 as part of the PSS at the University of Bath.
Abstract: After introducing one of the most important concepts of mathematical finance, the fundamental theorem of asset pricing (FTAP) and the related no arbitrage pricing theory (NAPT), I will briefly discuss the main techniques and tools extensively used in option pricing, namely Monte Carlo, Fourier Transform and PDE methods. In order to give a fairly well-structured overview of a great chunk of currently preferred models, through a simple example the hierarchy of the mathematical models will be demonstrated by going from the basic Black-Scholes to some more advanced models, e.g. Stochastic Volatility with jumps. (Even those people, who are familiar with these concepts, might find the main focus, i.e. structured overview, of this talk beneficial).