Small-maturity asymptotics for the at-the-money implied volatility slope in 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 behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money 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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
- Aleksandar Mijatovi\'c & Peter Tankov, 2012. "A new look at short-term implied volatility in asset price models with jumps," Papers 1207.0843, arXiv.org, revised Jul 2012.
- Figueroa-López, José E. & Houdré, Christian, 2009. "Small-time expansions for the transition distributions of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3862-3889, November.
- Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1350001-1-1.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1310.3061. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.