I'm interested in the areas surrounding Stochastic Volatility Modelling. I've read up on the main models that are prominent in the literature (Hull White, Heston, SABR) but I was wondering what the other issues facing this field are.
Incorporating Stochastic Volatility makes an incomplete model and I've read a few papers on how one may potentially counteract this incompleteness. This also leads from the fact that there could be more than one EMM which turns the asset price process into a martingale, so I have also read up on choosing an optimal measure which is closest to the real world measure.
Does anyone know about other areas like the two I have mentioned which would be good to read up on to solidify my understanding of Stochastic Volatility?