The Small Maturity Implied Volatility Slope for L\'evy Models
We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the growth of the slope for infinite activity exponential Levy models. As auxiliary results, we obtain the limiting values of short maturity digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.
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- Michael Roper & Marek Rutkowski, 2009. "On The Relationship Between The Call Price Surface And The Implied Volatility Surface Close To Expiry," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 427-441.
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