Vehicle-to-vehicle (VTV) wireless communications have many envisioned applications in traffic safety and congestion avoidance, but the development of suitable communications systems and standards requires accurate models for the VTV propagation channel. In this paper, we present a new wideband multiple-input-multiple-output (MIMO) model for VTV channels based on extensive MIMO channel measurements performed at 5.2 GHz in highway and rural environments in Lund, Sweden. The measured channel characteristics, in particular the nonstationarity of the channel statistics, motivate the use of a geometry-based stochastic channel model (GSCM) instead of the classical tapped-delay line model. We introduce generalizations of the generic GSCM approach and techniques for parameterizing it from measurements and find it suitable to distinguish between diffuse and discrete scattering contributions. The time-variant contribution from discrete scatterers is tracked over time and delay using a high resolution algorithm, and our observations motivate their power being modeled as a combination of a (deterministic) distance decay and a slowly varying stochastic process. The paper gives a full parameterization of the channel model and supplies an implementation recipe for simulations. The model is verified by comparison of MIMO antenna correlations derived from the channel model to those obtained directly from the measurements.