Due to its high sensitivity and minimal aliasing, the pyramid wavefront sensor (PyWFS) is becoming a popular choice for astronomical adaptive optics. To date, all implementations of the PyWFS modulate the input beam in order to operate the device the linear regime, however, this modulation reduces the sensitivity. Simulations in a recently published article show that model-based nonlinear estimation techniques can extend the range in which the PyWFS can be used without modulation, thus allowing modulation-free operation at lower Strehl values than previously thought possible. Further, the article shows that required calculations for the model-based nonlinear estimation do not require any real-time optical simulations and can be performed in massively parallel fashion, thus, (hopefully) allowing onsky implementation. The model-based estimation requires a realistic and phase-accurate, calibrated computational model (CCM) of the PyWFS. This article summarizes the potential benefits of modelbased nonlinear estimation and outlines a procedure to obtain the needed CCM.