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Local Volatility Models

Would you consider Heston, SABR, Black, or LMM as examples? If not, what are some examples of these?

My understanding is that 'local volatility models' are not separate models in and of themselves (as jmh530 points out) and they were used to price exotics while incorporating the skew using a simpler method than was available at the time.

What I think you might be getting at is understanding the differences/similarities between local, implied, and stochastic volatilities. HTH.

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