On the Implied Volatility Skew Outside the At-the-Money Point

The small-maturity implied volatility of an asset pricing model is fully determined by the asymptotics of traded option prices, and thus model-free expressions are available. We show how by sharpening one such expression it is possible to derive a general formula for the leading order of the in-the-money and out-of the money implied volatility skew. We apply this to the Heston model, exponential Lévy models and their time changes, as well as to some recently proposed pricing models with independent returns increments