Before revision:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .
After revision:  These behaviors are closely tied to the long-term growth rate of asset price momentsas well as implied volatility asymptotics in models where return of stock prices are modeled by affine processes whose exponential moments do not have an explicit formula .