Aims. We present the first theoretical SN Ia light curves calculated with the time-dependent version of the general purpose model atmosphere code PHOENIX. Our goal is to produce light curves and spectra of hydro models of all types of supernovae. Methods. We extend our model atmosphere code PHOENIX to calculate type Ia supernovae light curves. A simple solver was implemented which keeps track of energy conservation in the atmosphere during the free expansion phase. Results. The correct operation of the new additions to PHOENIX were verified in test calculations. Furthermore, we calculated theoretical light curves and compared them to the observed SN Ia light curves of SN 1999ee and SN 2002bo. We obtained LTE as well as NLTE model light curves. Conclusions. We have verified the correct operation of our extension into the time domain. We have calculated the first SN Ia model light curves using PHOENIX in both LTE and NLTE. For future work the infrared model light curves need to be further investigated.