• Aït-Sahalia, Y., and J. Jacod (2009): Estimating the Degree of Activity of Jumps in High Frequency Data, Ann. Stat. 37, 22022244.
  • Andersen, L., and A. Lipton (2013): Asymptotics for Exponential Lévy Processes and Their Volatility Smile: Survey and New Results, Int. J. Theor. Appl. Finance 16(1), 198.
  • Belomestny, D. (2010): Spectral Estimation of the Fractional Order of a Lévy Process, Ann. Stat. 38(1), 317351.
  • Blumenthal, R. M., and R. K. Getoor (1961): Sample Functions of Stochastic Processes with Stationary Independent Increments, J. Math. Mech. 10, 493516.
  • Carr, P., H. Geman, D. Madan, and M. Yor (2002): The Fine Structure of Asset Returns: An Empirical Investigation, J. Bus. 75(2), 305332.
  • Carr, P., and D. Madan (1998): Option Valuation Using the Fast Fourier Transform, J. Comput. Finance 2(2), 6173.
  • Carr, P., and L. Wu (2003): What Type of Process Underlies Options? A Simple Robust Test, J. Finance 58(6), 25812610.
  • Figueroa-López, J., and M. Forde (2012): The Small-Maturity Smile for Exponential Lévy Models, SIAM J. Financial Math. 3(1), 3365.
  • Friz, P., and S. Benaim (2009): Regular Variation and Smile Asymptotics, Math. Finance 19(1), 112.
  • Gao, K., and R. Lee (2011): Asymptotics of Implied Volatility to Arbitrary Order. Preprint.
  • Gatheral, J. (2006): The Volatility Surface: A Practitioner's Guide, Hoboken, NJ: Wiley Finance.
  • Gulisashvili, A. (2010): Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes, SIAM J. Financial Math. 1(1), 609641.
  • Houdré, C., R. Gong, and J. Figueroa-López (2011): High-Order Short-Time Expansions for ATM Option Prices under the CGMY Model. Preprint.
  • Jacod, J., and A. N. Shiryaev (2003): Limit Theorems for Stochastic Processes, 2nd ed., Berlin: Springer.
  • Jacquier, A., M. Keller-Ressel, and A. Mijatović (2013): Large Deviations and Stochastic Volatility with Jumps: Asymptotic Implied Volatility for Affine Models, Stochastics 85(2), 321345.
  • Lee, R. (2004): The Moment Formula for Implied Volatility at Extreme Strikes, Math. Finance 14(3), 469480.
  • Muhle-Karbe, J., and M. Nutz (2011): Small-Time Asymptotics of Option Prices and First Absolute Moments, J. Appl. Probab. 48(4), 10031020.
  • Protter, P. (2004): Stochastic Integration and Differential Equations, 2nd ed., Berlin: Springer.
  • Roper, M. (2009): Implied Volatility: Small Time to Expiry Asymptotics in Exponential Lévy Models. PhD thesis, University of New South Wales.
  • Roper, M., and M. Rutkowski (2009): On the Relationship between the Call Price Surface and the Implied Volatility Surface Close to Expiry, Int. J. Theor. Appl. Finance 12(4), 427441.
  • Rüschendorf, L., and J. H. Woerner (2002): Expansion of Transition Distributions of Lévy Processes in Small Time, Bernoulli 8(1), 8196.
  • Samorodnitsky, G., and M. Taqqu (1994): Stable Non-Gaussian Random Processes, New York: Chapman & Hall.
  • Sato, K. (1999): Lévy Processes and Infinitely Divisible Distributions, Cambridge, UK: Cambridge University Press.
  • Tankov, P. (2010): Pricing and Hedging in Exponential Lévy Models: Review of Recent Results, in Paris-Princeton Lecture Notes in Mathematical Finance, R. Carmona and N. Touzi, eds., Vol. 2003 of Lecture Notes in Mathematics. Berlin: Springer.
  • Tehranchi, M. R. (2009): Asymptotics of Implied Volatility Far from Maturity, J. Appl. Probab. 46(3), 629650.
  • Wang, I., J. Wan, and P. Forsyth (2007): Robust Numerical Valuation of European and American Options under the CGMY Process, J. Comput. Finance 10(4), 3169.