Non-Affine Term-Structure Models and Short-Rate Models with Stochastic Jump Intensity

Abstract

Although the model setup proposed in this thesis is of the exponential-affine class, we can also extend the framework to allow for certain non-affine models and models with state-dependent jump intensities λ^ℚ(x _t ). Moreover, option prices under these more sophisticated model dynamics can be priced in our numerical scheme without greater effort, due to an exponential separable structure of the governing characteristic function. However, working with a non-affine model, we have to abandon jump components for those particular non-affine factors. A stochastic jump intensity in the general exponentialaffine model framework is introduced in Duffie, Pan and Singleton (2000). Consequently, the jump transform is no longer independent of the coefficient function a(z, τ), and therefore a complicated system of ODEs has to be determined numerically anyway. Since both approaches need to establish further restrictions, they are only discussed as possibilities for extending and modifying the base model, respectively.