Given known call option prices, there is a unique local volatility function consistent with those prices.
So why use stochastic volatility models? We can use the market to find local volatility, and then that's our model, no?
Why do we need to complicate things by introducing a stochastic volatility model?
Doesn't that also mean that we need to find a model that produces the same local volatility given by Dupire's equation, since otherwise it would not match the market prices. How is there any guarantee it does that?