I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/surface calibrated only on ITM and ATM quotes? I think that it's going to somehow underestimate/overestimate the real volatility in ITM and OTM regions. Will these effects be the same for all smile models? What if one would calibrate it on OTM and ATM without ITM? I'm looking for either quantitative or qualitative explanation.
UPD: I'm talking about a market where there is only one significant market maker providing indicative quotes for caps/floors and there are usually no more than 2-3 trades made per week, so there is no opportunity to calibrate a model to real trades. The interest rate was roughly 5% and the market maker was providing quotes for 4% floors as well as ATM, 6%, 8%, 10% caps. However due to the global inflation current ATM is already set at 12-13% with fixed strikes staying the same, i.e. 6%, 8%, 10% caps are ITM and 4% floor is OTM.