Hello,Could someone explain the strengths and weaknesses of local volatility versus stochastic volatility?When for example one would use local volatility instead of stochastic vol?Thanks,

Local vol models are quite hard to stabilize. Since you only have discrete data (volsurface points), the implementation depends on the interpolation technique you use to connect those discrete points. Suppose you get this to work (it can be done), then you have a model that reproduces your plain vanilla options.On the other hand, if you take a stochastic vol model, you immediately have a model-price for the complete range of strikes and maturities. However, there is a small calibration error (depends on the model how small this is going to be). This means that the model is not capable of reproducing the market values. However, if the error is in the bid-offer range, this is not too bad.So, suppose you have to choose between those two... If you only want to price plain vanilla options, both models will do. If you go to the range of far OTM options, stochastic vol models might be preferred since they are arbitrage-free. Now, if you want to price exotics, bear in mind that local-vol models have flattening forward skew. This means that if you price forward-start options, the skew that the local-vol will price in will be quite low. No trader would believe this. Therefore, it is generally accepted that local-vol models are not that good. Of course, it all depends on what you want to be doing with the model.I personally, prefer stochastic vol models. But I know some other quants who are quite fond of local vol... It might be a matter of taste?