  We consider implied volatilities in asset pricing models, where the
discounted underlying is a strict local martingale under the pricing measure.
Our main result gives an asymptotic expansion of the right wing of the implied
volatility smile and shows that the strict local martingale property can be
determined from this expansion. This result complements the well-known
asymptotic results of Lee and Benaim-Friz, which apply only to true
martingales. This also shows that `price bubbles' in the sense of strict local
martingale behaviour can in principle be detected by an analysis of implied
volatility. Finally we relate our results to left-wing expansions of implied
volatilities in models with mass at zero by a duality method based on an
absolutely continuous measure change.
