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I have been doing a project about modeling with the CEV process (dS = a S^b dW). My question is whether this is really used in the markets for anything, or whether it is just a toy model / historical curiosity / special case of SABR.Thanks,

I like the constant elasticity volatility idea, and often use it for investigation. However, I haven't seen it used in practice, that is for pricing an instrument or setting a hedge ratio, for at least ten years. That doesn't mean people don't use it somewhere, but it's not common.

Thanks for the reply Aaron. Any favorite papers or suggested avenues to pursue? I have done a fairly thorough search already, but more ideas welcome!

If you have read the original Cox and Ross paper (Journal of Financial Economics, March 1976) then I don't know of any major improvement.

I like this paper-V

The other nice one is "Computing the Constant Elasticity of Variance Option Pricing Formula" by Mark Schroder