Hello, I have some questions about implied risk neutral density. Here are my understandings, correct me if I am wrong. 1. Purposes of computing implied risk neutral density (RND): a) Practitioners use available options to get some inferences to stock prices (distribution/dynamics) so that they can price options (with maturity/strike currently not available from the market) or a larger class of options. b) to backtest if the option prices are correct or their models are correct? 2. Figlewski2008 shows that we can get the RND model free. However, we can not interpolate call price in strikes in practice. Instead he suggest interpolating vols to get vol smile through BS model. The problem here is we have assumed BS model which voilates the model free feature. Does the result make any sense here? How pratitioners deal with this? 3. Whare are the procedures to do 1 a? Of course we can not get a perfect time dependent RND. We want to build up BS and non-BS models to price options. Do we calibrate the parameters from the limited existing option prices? 4. It seems pratitioners do not deal with RNDs, they always talk about vols. If we talk about vols, then there must be a model behind, which is BS? Then what happens if they want to use different models? Are they transforming/matching the vol smile/surface (BS by default) to a new vol smile/surface suggested by non-BS models?

Both parameterized stochastic process models and 'fitting models' yield risk-neutral densities.The simplest semi-decent procedure (at a single expiration): fit Gatheral's SVI model and then use the Breeden-Litzenberger relation with the chain rule. This is a fitting model.