Transform analysis of affine jump diffusion processes with applications to asset pricing

This work presents a class of models in asset pricing, whose underlying has dynamics of Affine jump diffusion type. We first present L´evy processes with their properties. We then introduce Affine jump diffusion processes whichare basically a particular class of L´evy processes. Our motivation for theseis driven by the fact that many financial models are built on them. Affinejump diffusion processes present good analytical properties that allow one toget close form formulas for a wide range of option pricing. The approach we use here is based on the paper by Duffie D, Pan J, andSingleton K. An example will show how incorporating parameters such asthe volatility of the underlying asset in the model, can influence the resultingprice of the financial instrument under consideration. We will also show howthis class of models incorporate well known models, specially those used tomodel interest rates dynamics, like for instance the Vasicek model. © University of Pretoria 2008 E992/gm