This series of lectures considers the modeling of term structures on different markets. The starting point is the classical approach from Heath, Jarrow and Morton (1992). We extend the framework sequently to more general settings allowing the driving process to be a general semimartingale. This leads to interesting questions of existence, consistency and invariant measures which shall be treated.

Besides having a general framework, for practical applications models are needed which have nice numerical properties. We will study market models along the lines of Brace, Gatarek and Musiela (1995) and affine models as in Duffie, Filipovic and Schachermayer (2003).

Thereafter we consider the application of this framework to different markets. One particular case which will be studied is the application to CDO markets, where we follow Filipovic, Overbeck and Schmidt (2009). For practical applications, affine models as well as market models will be studied.

We will conclude with an overview on further markets, like electricity markets, and give a short sketch on the difficulties arising.