I am trying to understand the term level dependence of volatility as mentioned in Pricing of options on assets with level dependent stochastic volatility. Is this same as leverage effect mentioned in Empirical properties of asset returns: stylized facts and statistical issues ?
Leverage effect means that the volatility of an asset is negatively correlated with the returns of that asset. This seems to suggest the presence of "volatility skew" implied volatility vs strike price. Is this a correct interpretation ?
If yes, How do we compare this with the observation of "volatility smile" in implied volatility vs strike price ?