Short-time at-the-money skew and rough fractional volatility

References

• Aït-Sahalia, Y. and Jacod, J., Testing for jumps in a discretely observed process. Ann. Stat., 2009, 37, 184–222.
   Web of Science ®Google Scholar
• Alòs, E., León, J.A. and Vives, J., On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility. Finance Stoch., 2007, 11, 571–589.
   Web of Science ®Google Scholar
• Armstrong, J., Forde, M., Lorig, M. and Zhang, H., Small-time asymptotics for a general local-stochastic volatility model with a jump-to-default: Curvature and the heat kernel expansion. 2014, arXiv:1312.2281.
   Google Scholar
• Bayer, C., Friz, P.K. and Gatheral, J., Pricing under rough volatility. 2015, SSRN:2554754.
   Google Scholar
• Berestycki, H., Busca, J. and Florent, I., Computing the implied volatility in stochastic volatility models. Commun. Pure Appl. Math., 2004, 57(10), 1352–1373.
   Web of Science ®Google Scholar
• Bergomi, L., Smile dynamics II. Risk Mag., 2005, October, 67--73. Also available at SSRN:1493302.
   Google Scholar
• Billingsley, P., Convergence of Probability Measures, 2nd ed., 1999 (A Wiley-Interscience Publication, John Wiley & Sons Inc: New York).
   Google Scholar
• Dupire, B., Pricing with a smile. Risk Mag., 1994, January, 18–20.
   Google Scholar
• Figueroa-López, J.E. and Ólafsson, S., Short-time asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps. 2015, arXiv:1502.02595.
   Google Scholar
• Forde, M. and Jacquier, A., Small-time asymptotics for implied volatility under a general local-stochastic volatility model. Appl. Math. Finance, 2011, 18, 517–535.
   Google Scholar
• Forde, M. and Zhang, H., Asymptotics for rough stochastic volatility models. Under revision at SIAM J. Finan. Math., 2015.
   Google Scholar
• Fouque, J.P., Papanicolaou, G. and Sircar, R., Derivatives in Financial Markets with Stochastic Volatility, 2000 (Cambridge University Press: Cambridge).
   Google Scholar
• Fouque, J.P., Papanicolaou, G., Sircar, R. and Solna, K., Multiscale stochastic volatility asymptotics. Multiscale Model. Simul., 2003, 2, 22–42.
   Web of Science ®Google Scholar
• Fouque, J.P., Papanicolaou, G., Sircar, R. and Solna, K., Maturity cycles in implied volatility. Finance Stoch., 2004, 8, 451–477.
   Web of Science ®Google Scholar
• Fukasawa, M., Asymptotic analysis for stochastic volatility: Martingale expansion. Finance Stoch., 2011a, 15, 635–654.
   Web of Science ®Google Scholar
• Fukasawa, M., Asymptotic analysis for stochastic volatility: Edgeworth expansion. Electron. J. Probab., 2011b, 16, 764–791.
   Web of Science ®Google Scholar
• Garnier, J. and Solna, K., Correction to Black--Scholes formula due to fractional stochastic volatility. 2015, arXiv:1509.01175.
   Google Scholar
• Gatheral, J., The Volatility Surface: A Practioner’s Guide, 2006 (John Wiley & Sons Inc: Hoboken, NJ).
   Google Scholar
• Gatheral, J., Hsu, E., Laurence, P., Ouyang, C. and Wang, T.-H., Asymptotics of implied volatility in local volatility model. Math. Finance, 2012, 22(4), 591–620.
   Web of Science ®Google Scholar
• Gatheral, J., Jaisson, T. and Rosenbaum, M., Volatility is rough. 2014, SSRN:2509457.
   Google Scholar
• Guennoun, H., Jacquier, A. and Roome, P., Asymptotic behaviour of the fractional Heston model. 2014, arXiv:1411.7653.
   Google Scholar
• Henry-Labordére, P., Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing, 2009 (Chapman & Hall).
   Google Scholar
• Kunitomo, N. and Takahashi, A., On validity of the asymptotic expansion approach in contingent claim analysis. Ann. Appl. Probab., 2003, 13(3), 914–952.
   Web of Science ®Google Scholar
• Lamberton, D. and Lapeyre, B., Introduction to Stochastic Calculus Applied to Finance, 1996 (Chapman & Hall: London).
   Google Scholar
• Lewis, A.L., Option Valuation under Stochastic Volatility, 2000 (Finance Press: Newport Beach, CA).
   Google Scholar
• Medvedev, A. and Scaillet, O., Approximation and calibration of short-term implied volatilities under jump-diffusion stochastic volatility, 2006. Swiss Finance Institute Research Paper Series Number 06–8.
   Google Scholar
• Mijatović, A. and Tankov, P., A new look at short-term implied volatility in asset price models with jumps. Math. Finance, 2013, 26(1), 149–183. doi:10.1111/mafi.12055.
   Web of Science ®Google Scholar
• Muravlev, A.A., Representation of a fractional Brownian motion in terms of an infinite-dimensional Ornstein--Uhlenbeck process. Russ. Math. Surv., 2011, 66(2), 439–441.
   Web of Science ®Google Scholar
• Nourdin, I., Selected Aspects of Fractional Brownian Motion, 2012 (Springer-Verlag: Italia).
   Google Scholar
• Novikov, A., Analysis and simulation of models with fractional Brownian process in finance and statistics, the first plenary talk at Winter Workshop on Finance (16--17 February 2014), Hokkaido University, 2014.
   Google Scholar
• Osajima, Y., The asymptotic expansion formula of implied volatility for dynamic SABR model and FX hybrid model. 2006, UTMS 2006–29, The University of Tokyo.
   Google Scholar
• Osajima, Y., General asymptotics of Wiener functionals and application to mathematical finance. 2007, UTMS 2007–10, The University of Tokyo.
   Google Scholar
• Pham, H., Large deviations in mathematical finance. Lecture note, 2010. Available online at: http://www.proba.jussieu.fr/pageperso/pham/GD-finance.pdf.
   Google Scholar
• Yoshida, N., Asymptotic expansion for statistics related to small diffusions. J. Jpn. Stat. Soc., 1992, 22, 139–159.
   Google Scholar