We perform a theoretical study of carrier transport effects in the frequency modulation response of single-mode quantum well (QW) lasers under both small and large signal modulations. The lasers considered are ultra-high speed InGaAs/GaAs MQW lasers with intrinsic modulation bandwidth of 40 GHz. A rate-equation model, including spontaneous emission noise, for the carriers in the active region (quantum wells) Nw, the carriers in the separate confinement heterostructure and in the barriers (core) Nc and for the optical field is used. Carrier transport effects are included by considering two effective time constants: the transport/capture time, and the re-emission time out of the QW's (escape time). We also consider the change in the laser frequency due to the refractive index changes in both the wells and the core. In the wells the laser frequency increase with Nw is described by the linewidth enhancement factor. Since the laser frequency is below the bandgap in the core, the refractive index change with Nc, dnc/dNc, can be positive or negative depending on the doping level. When dnc/dNc > 0 the magnitude of the FM response decreases when the capture (escape) time increases (decreases), but the shape is flat. We have also studied the frequency statistics under large signal modulation. A linear relationship between frequency chirp range and turn-on time is obtained, as in bulk lasers. For QW lasers biased below threshold the chirp range is found to increase (decrease) for large capture times when dnc/DNc is positive (negative) due to the contribution of the carriers in the core. The opposite behavior is found for small escape times.