I am presently engaged in a project wherein my objective is to construct a volatility surface utilizing either the SVI parameterization or the SABR model, leveraging real market data. Initially, I used mid/mark implied volatility for the purpose of calibration, yielding relatively satisfactory fit. However, my calibration attempts using ask_iv or bid_iv have yielded very bad fits.
I find myself in a state of uncertainty as to the underlying reasons for these subpar calibrations when utilizing ask or bid implied volatility. Logically, it stands to reason that individuals engaged in trading activities would typically reference either ask or bid implied volatility when executing their orders. Consequently, I am curious if there exist specific guidelines or best practices that one should adhere to when fitting the volatility surface with ask/bid_iv data. Furthermore, I am interested in understanding how market participants make trading decisions based on a volatility surface calibrated using mid/mark_iv. It's pertinent to mention that the options I am dealing with are relatively illiquid.
I would greatly appreciate any references to books, research papers, blogs, or any resources that delve into this subject matter, as they would prove invaluable to my project.