Damir Filipovic, ETH Zürich
An affine process (AP) is a Markov process with the property that, for every , the characteristic function of is an exponential-affine function of the initial state . 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.