# What is price level dependence of volatility

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 ?

• In this paper the random movement in stock prices is $\sigma S^{\alpha}dZ$. For $\alpha=1$ this is the same as Black Scholes constant vol GBM. But for other values of alpha the volatility increases ($\alpha>1$) or decreases with stock price. It could be one way to model the leverage effect, but not the only one. For example the GJR model of volatility is another way. The leverage effect is an empirical proeprty of stock prices but not a model per se. – noob2 Aug 2 '18 at 12:05