Visible light communications (VLC) have attracted considerable interest in recent years due to an increasing need for data communication links in home and enterprise environments. Organic light-emitting diodes (OLEDs) are widely used in display applications owing to their high brightness, high quality colour-rending capability and low cost. As a result, they are attractive candidates for the implementation of ultra-low cost visible light optical links in free-space and guided-wave communications. However, OLEDs need to exhibit a bandwidth of at least ~MHz to be able to support the modest data rates (~Mbps) required in these applications. Although fluorescent OLEDs typically exhibit shorter photon lifetimes than inorganic LEDs, the bandwidth performance of the large size OLEDs used in display applications are limited by their electrical characteristics. In this work, we present a detailed physical simulation that describes well the performance of fast OLED devices that exhibit significant -3 dB bandwidths (f3dB) of 44 MHz obtained for a 0.12 mm2 device. It is demonstrated that the reduction of the device size results in a significant bandwidth improvement due primarily to a reduction in parasitic capacitance of the devices, though this is counteracted by carrier dynamic effects. The model provides an insight into the basic physical properties of the OLED and may be used for optimisation of future generations of OLED devices.