Novel technologies aiming at improving target dose coverage while minimising dose to organs at risk use delivery of radiation fields that significantly deviate from reference conditions defined in protocols such as TG-51 and TRS-398. The use of ionization chambers for patient-specific quality assurance of these new delivery procedures calibrated in reference conditions increases the uncertainties on dose delivery. The conversion of the dose to the chamber cavity to the dose to water becomes uncertain; and the geometrical details of the chamber, as well as the details of the delivery, are expected to be significant. In this study, a realistic model of the Exradin® A12 Farmer chamber is simulated. A framework is applied for the calculation of ionization chamber response to arbitrarily modulated fields as a summation of responses to pencil beams. This approach is used with the chamber model and tested against measurements in static open fields and dynamic MLC IMRT fields. As a benchmark test of the model, quality conversion factors values calculated by Monte-Carlo simulation with the chamber model are in agreement within 0.1 % and 0.4 % with those in the AAPM TG-51, for 6 MV and 18 MV photon beams, respectively. Pencil-beam kernels show a strong dependence on the geometrical details of the chamber. Kernel summations with open fields show a relative agreement within 4.0 % with experimental data; the agreement is within 2.0 % for dynamic MLC IMRT beams. Simulations show a strong sensitivity of chamber response on positioning uncertainties, sometimes leading to dose uncertainties of 15 %.