Before revision:  Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the point of view of option prices. For infinite variation processes , the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the finite variation case , the wings have a constant model-independent slope.
After revision:  Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter , the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the finite variation case , the wings have a constant model-independent slope.