15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Minisymposium Finanzmathematik
Donnerstag, 20. September 2001, 16.10, Audimax der Universität Wien


Affine Processes and their Applications in Finance

Damir Filipovic, ETH Zürich


An affine process (AP) $ X$ is a Markov process with the property that, for every $ t$, the characteristic function of $ X_t$ is an exponential-affine function of the initial state $ X_0$. We discuss several consequences of this definition. It can be shown that any AP is a Feller jump-diffusion process with an affine generator. In the case where the state space D is the real line, an AP is simply an Ornstein-Uhlenbeck type process. If D is the positive half-line, an AP turns out to be a CBI (continuous state branching with immigration)-process.

APs are widely used in financial applications, which is due to their analytical tractability. We give a short overview of the classical papers in the areas: term structure modelling, stochastic volatility option pricing and intensity based modelling of default.

E-Mail: filipo@math.ethz.ch
Homepage: www.math.ethz.ch/~filipo

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