There is much evidence about the correlation between spot price and option implied vol in the empirical. This is very important in risk management(i.e. delta hedge). I want to know how to add this correlation to vol curve and how to use this curve for risk management.
For example, I calibrate a Heston model from listed options, and get $\rho$ parameter(correlation between $dW_{spot}$ and $dW_{\sigma}$). Does this parameter have any practical significance? If so, how to use this parameter to adjust option delta, or even curve skew. If not, how to make the curve reflect this property.
