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 and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics at large-time-to-maturity or at extreme strikes for any given option maturity .