  In this paper, we obtain asymptotic formulas with error estimates for the
implied volatility associated with a European call pricing function. We show
that these formulas imply Lee's moment formulas for the implied volatility and
the tail-wing formulas due to Benaim and Friz. In addition, we analyze
Pareto-type tails of stock price distributions in uncorrelated Hull-White,
Stein-Stein, and Heston models and find asymptotic formulas with error
estimates for call pricing functions in these models.
