Empirical evidence shows that calibrating exponential Lévy models by options with different maturities leads to conflicting information. In other words, the stationarity implicitly assumed in the exponential Lévy model is not satisfied. An identifiable time-inhomogeneous Lévy model is proposed that does not assume stationarity and that can integrate option prices from different maturities and different strike prices without leading to conflicting information. In the time-inhomogeneous Lévy model, the convergence rates are derived, and confidence intervals are shown for the estimators of the volatility, the drift, the intensity and the Lévy density. Previously, confidence intervals have been constructed for time-homogeneous Lévy models in an idealized Gaussian white noise model. In the idealized Gaussian white noise model, it is assumed that the observations are Gaussian and given continuously across the strike prices. This simplifies the analysis significantly. The confidence intervals are constructed in a discrete observation setting for time-inhomogeneous Lévy models, and the only assumption on the errors is that they are sub-Gaussian. In particular, all bounded errors with arbitrary distributions are covered. Additional results on the convergence rates extend existing results from time-homogeneous to time-inhomogeneous Lévy models.