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 novel general formula for the leading order of the in-the-money and out-of-the money (ITM/OTM) implied volatility skew. We apply this formula to find expressions of the small maturity limiting skew of the Heston stochastic volatility model, of exponential L & eacute;vy models and their time changes, as well as that of some recently proposed pricing models with independent log returns.