Before revision:  Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets  . A precise characterization of the hedging cost, the replication cost caused by the volatility fluctuations, is presented in an asymptotic regime of rapid mean reversion for the volatility fluctuations.
After revision:  Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options . A precise characterization of the hedging cost, the replication cost caused by the volatility fluctuations, is presented in an asymptotic regime of rapid mean reversion for the volatility fluctuations.