  We develop a general term structure framework taking stochastic
discontinuities explicitly into account. Stochastic discontinuities are a key
feature in interest rate markets, as for example the jumps of the term
structures in correspondence to monetary policy meetings of the ECB show. We
provide a general analysis of multiple curve markets under minimal assumptions
in an extended HJM framework and provide a fundamental theorem of asset pricing
based on NAFLVR. The approach with stochastic discontinuities permits to embed
market models directly, unifying seemingly different modeling philosophies. We
also develop a tractable class of models, based on affine semimartingales,
going beyond the requirement of stochastic continuity.
