large amount of jumps or, more generally, rapid changes in stock prices or other financial time series occur in correspondence with announcements released at scheduled and hence predictable times (see, e.g., [@Johannes2004]). A prominent example is the jump of the EUR/GBP exchange rate on the 23rd of June in 2016 when it became clear that the British referendum on membership in the EU will come out in favor of Brexit. In addition, large jumps in stock prices frequently coincide with the release of quarterly reports or earnings announcements. (See Figure \[fig:db\] for an example and [@DupireTalk2017] for further empirical support). Econometric models incorporating such jumps at predetermined times were studied and tested on market data in [@Piazzesi2001], see also [@Piazzesi2010] and [@GehmlichSchmidt2015MF; @FontanaSchmidt2016].

While affine processes are a prominent model class for interest rates or stochastic volatility, they have only been considered under the assumption of stochastic continuity, which precludes jumps at predictable times. This assumption is dropped in this paper, and we study affine processes only under very mild assumptions, which allow for jumps to occur at both predictable and totally inaccessible times.

The defining property of affine processes is the exponential affine form of the conditional characteristic function 