Newbie here with basic questions. I have researched the topic online, but am still at a loss. I went through a nice course on calibration, saw how to apply stochastic short rate, stochastic vol, jump diffusion and calibrate modeled prices and IV to actual market prices. However, I would love to understand:
1- The actual applications of this modeling when trading trading vanilla options, if any.
2- How does a calibrated surface help (as an input?) in predicting IV skew and term in next periods, if applicable? For IVs i would assume the only thing that matters is that we stick to one model.
3- Is a calibrated surface model necessary to infer proper greeks, vs BSM for instance
4- Are there more direct ways to fit an IV surface to observe its variations over time?
Any input appreciated!