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

Term structure modeling for multiple curves with stochastic discontinuities