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Are you able to provide some suggestions for resources to get started with non-flat volatility modelling? The models I am interested in are the likes of CEV, Heston, SABR etc.

I have tried looking into Gatheral's The volatility surface. A practitioner's guide but it is a little too heavy so looking for something ideally more approachable.

I am looking for "first course in local and stochastic volatility modelling" really to get me started in this space. Thanks in advance for recommendations!

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If you are looking for a short introduction into various concepts used in volatility modeling without too much mathematical derivations (although written by a mathematician), I would recommend 'Smile pricing explained' by Peter Austing, Palgrave Macmillan (2014). It's a good first book to read and helpful in the future when you read more advanced books (like Gatheral).

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You may find A Short Note on Volatility Models an interesting summary providing bird's-eye overview of general ideas in volatility modeling.

I would highly recommend SABR and SABR LIBOR Market Models in Practice as a great reference to SABR and SABR LMM accessible without prior knowledge of these models.

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