Hello,I'm currently straggling with Delta hedging under SABR model (or other stochastic volatility models). As far as I know there are numerous Delta hedging strategies theoretically and practically such as Hagan's delta proposed in his original paper, Bartlett's delta known as minimum variance delta as detailed in "Hedging under the SABR model", ect.My question is how practitioners are typically doing with delta hedging exotic options under SABR model. Are they simply using minimum variance delta?Thanks!

Let me express a few thoughts about hedging under SABR. Let for simplicity sigma takes two values sigma_1 , sigma_2 with a known distribution and sigma independent on Wiener process W. Then for each value of sigma there exist BSE solution which represents call option price for chosen sigma. Exchange BSE solutions two market scenarios option price with sigma_1 , sigma_2 for other BSE solution which uses sigma_implied violates hedging for either market case sigma_1 or sigma_2. Though we can estimate value of the risk implied by the replacement of real sigmas on sigma_implie. In continuous time sigma situation is similar but more complex for calculations.

I think he said practical help....(I have no experience of SABR so cannot offer it myself, gcgamet, apologies)

If you really believe the model you use and all its parameters, then I suppose you can take the delta implied by the model. Others may price using advançed model but then express the model price in terms of a Black Scholes price (using sth called implied volatility) and then delta hedge based on the resulting BS delta. Sometimes you may even want to deviate from the delta implied by the model if you have a view on the underlying real world drift. So there probably isn't one answer to your question.

Elsewhere in another thread I commented in someone argued that it makes a lot of sense to use a stochastic vol model to hedge an FX options book, so there may be some scope for hedging with such models. In my experience, in the USD market at least, the SABR model is used mostly for marking the options skew. It's also an indicator of your book's vega risk (both to ATM vol and skew parameters). However the delta hedging problem is until further notice heuristic. If you think about it, the SABR model is a completely idiotic model in terms of economic content. There isn't anything in there. It may be complicated to solve mathematically, but that doesn't make it a good model. The rules governing the volatility backbone are manifold and weak, so trying to capture them in such a model is a fallacy at best. I think that delta hedging is more like a data science problem, than a physical sciences problem.Anyway, so as far as I know people don't delta hedge against SABR, but practice shadow delta hedging.

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See this link.