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The Wide-Area Linear Optical Polarimeter (WALOP)-South instrument is an upcoming wide-field and high-accuracy optical polarimeter to be used as a survey instrument for carrying out the Polar-Areas Stellar Imaging in Polarization High Accuracy Experiment (PASIPHAE) program. Designed to operate as a one-shot four-channel and four-camera imaging polarimeter, it will have a field of view of $35\times 35$ arcminutes and will measure the Stokes parameters $I$, $q$, and $u$ in a single exposure in the SDSS-r broadband filter. The design goal for the instrument is to achieve an overall polarimetric measurement accuracy of 0.1 % over the entire field of view. We present here the complete polarimetric modeling of the instrument, characterizing the amount and sources of instrumental polarization. To accurately retrieve the real Stokes parameters of a source from the measured values, we have developed a calibration method for the instrument. Using this calibration method and simulated data, we demonstrate how to correct instrumental polarization and obtain 0.1 % accuracy in the degree of polarization, $p$. Additionally, we tested and validated the calibration method by implementing it on a table-top WALOP-like test-bed polarimeter in the laboratory., Comment: 34 pages, 24 figures. Accepted for publication in the Journal of Astronomical Telescopes, Instruments, and Systems