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Research Papers

Short-time near-the-money skew in rough fractional volatility models

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Pages 779-798 | Received 22 Mar 2017, Accepted 07 Sep 2018, Published online: 13 Nov 2018

References

  • 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(4), 571–589. doi: 10.1007/s00780-007-0049-1
  • Azencott, R., Formule de Taylor stochastique et développement asymptotique d'intégrales de Feynman. In Seminar on Probability, XVI, Supplement, volume 921 of Lecture Notes in Math., pp. 237–285, 1982 (Springer: Berlin-New York).
  • Azencott, R., Petites perturbations aléatoires des systemes dynamiques: développements asymptotiques. Bull. Sci. Math., 1985, 109(3), 253–308.
  • Baudoin, F. and Ouyang, C., On small time asymptotics for rough differential equations driven by fractional Brownian motions. In Large Deviations and Asymptotic Methods in Finance, edited by P.K. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, and J. Teichmann, pp. 413–438, 2015 (Springer International Publishing: Cham).
  • Bayer, C., Friz, P.K., Gassiat, P., Martin, J. and Stemper, B., A regularity structure for rough volatility. Preprint, 2017. arXiv:1710.07481.
  • Bayer, C., Friz, P.K. and Gatheral, J., Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904. doi: 10.1080/14697688.2015.1099717
  • Ben Arous, G., Methods de Laplace et de la phase stationnaire sur l'espace de Wiener. Stochastics, 1988, 25(3), 125–153. doi: 10.1080/17442508808833536
  • Bennedsen, M., Lunde, A. and Pakkanen, M.S., Decoupling the short- and long-term behavior of stochastic volatility. Preprint, 2016. arXiv:1610.00332.
  • Bennedsen, M., Lunde, A. and Pakkanen, M.S., Hybrid scheme for Brownian semistationary processes. Finance Stoch., 2017, 21(4), 931–965. doi: 10.1007/s00780-017-0335-5
  • Bismut, J.-M., Large Deviations and the Malliavin Calculus. Progress in Mathematics, Vol. 45. 1984 (Birkhäuser Boston, Inc.: Boston, MA).
  • Carlen, E. and Kree, P., Estimates on iterated stochastic integrals. Ann. Probab., 1991, 19(1), 354–368. doi: 10.1214/aop/1176990549
  • Cass, T. and Friz, P., Densities for rough differential equations under Hörmander's condition. Ann. Math., 2010, 0, 2115–2141. doi: 10.4007/annals.2010.171.2115
  • Decreusefond, L., Stochastic integration with respect to Volterra processes. Ann. l. H. Poincare Probab. Statist., 2005, 41(2), 123–149. doi: 10.1016/j.anihpb.2004.03.004
  • Deuschel, J.-D., Friz, P.K., Jacquier, A. and Violante, S., Marginal density expansions for diffusions and stochastic volatility I: Theoretical foundations. Comm. Pure Appl. Math., 2014a, 67(1), 40–82. doi: 10.1002/cpa.21478
  • Deuschel, J.-D., Friz, P.K., Jacquier, A. and Violante, S., Marginal density expansions for diffusions and stochastic volatility II: Applications. Comm. Pure Appl. Math., 2014b, 67(2), 321–350. doi: 10.1002/cpa.21483
  • Deuschel, J.-D. and Stroock, D.W., Large Deviations, Vol. 137, 1989 (Academic Press: Boston, MA).
  • El Euch, O. and Rosenbaum, M., The characteristic function of rough Heston models. Preprint, 2016. To appear in Math. Finance.
  • Forde, M. and Jacquier, A., Small-time asymptotics for implied volatility under the heston model. Int. J. Theoret. Appl. Finance, 2009, 12(06), 861–876. doi: 10.1142/S021902490900549X
  • Forde, M. and Zhang, H., Asymptotics for rough stochastic volatility models. SIAM J. Financ. Math., 2017, 8(1), 114–145. doi: 10.1137/15M1009330
  • Friz, P.K. and Gassiat, P., Martingality and moments for lognormal rough volatility. In preparation, 2018.
  • Friz, P.K., Gerhold, S. and Pinter, A., Option Pricing in the Moderate Deviations Regime. Math. Finance, 2018, 28(3), 962–988. doi: 10.1111/mafi.12156
  • Friz, P. and Hairer, M., A Course on Rough Paths, 2014 (Springer: Cham).
  • Fukasawa, M., Asymptotic analysis for stochastic volatility: martingale expansion. Finance Stoch., 2011, 15(4), 635–654. doi: 10.1007/s00780-010-0136-6
  • Fukasawa, M., Short-time at-the-money skew and rough fractional volatility. Quant. Finance, 2017, 17(2), 189–198. doi: 10.1080/14697688.2016.1197410
  • Gao, K. and Lee, R., Asymptotics of implied volatility to arbitrary order. Finance Stoch., 2014, 18(2), 349–392. doi: 10.1007/s00780-013-0223-6
  • Gatheral, J., The Volatility Surface: A Practitioner's Guide, 2011 (John Wiley & Sons: Hoboken, NJ).
  • Gatheral, J., Jaisson, T. and Rosenbaum, M., Volatility is rough. Preprint, 2014. To appear in Quant. Finance.
  • Guennoun, H., Jacquier, A. and Roome, P., Asymptotic behaviour of the fractional Heston model. Preprint, 2014. arXiv:1411.7653.
  • Gulisashvili, A., Large deviation principle for Volterra type fractional stochastic volatility models. ArXiv e-prints, October 2017. To appear in SIAM J. Financ. Math.
  • Inahama, Y., Laplace approximation for rough differential equation driven by fractional brownian motion. Ann. Probab., 2013, 41(1), 170–205. doi: 10.1214/11-AOP733
  • Jacquier, A., Pakkanen, M.S. and Stone, H., Pathwise large deviations for the Rough Bergomi model. ArXiv e-prints, June 2017.
  • Jourdain, B., Loss of martingality in asset price models with lognormal stochastic volatility. Int. J. Theoret. Appl. Finance, 2004, 13, 767–787.
  • Lamperti, J., Semi-stable stochastic processes. Trans. Am. Math. Soc., 1962, 104(1), 62–78. doi: 10.1090/S0002-9947-1962-0138128-7
  • Lions, P.-L. and Musiela, M., Correlations and bounds for stochastic volatility models. Ann. Inst. H. Poincaré Anal. Non Linéaire, 2007, 24(1), 1–16.
  • Medvedev, A. and Scaillet, O., A simple calibration procedure of stochastic volatility models with jumps by short term asymptotics. Preprint, 2003. Available at SSRN 477441.
  • Medvedev, A. and Scaillet, O., Approximation and calibration of short-term implied volatilities under jump-diffusion stochastic volatility. Rev. Financ. Stud., 2007, 20(2), 427–459. doi: 10.1093/rfs/hhl013
  • Mijatović, A. and Tankov, P., A new look at short-term implied volatility in asset price models with jumps. Math. Finance, 2016, 26(1), 149–183. doi: 10.1111/mafi.12055
  • Muhle-Karbe, J. and Nutz, M., Small-time asymptotics of option prices and first absolute moments. J. Appl. Probab., 2011, 48(4), 1003–1020. doi: 10.1239/jap/1324046015
  • Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W (Eds.), NIST Handbook of Mathematical Functions, 2010 (Cambridge University Press: New York).
  • Osajima, Y., The asymptotic expansion formula of implied volatility for dynamic SABR model and FX hybrid model. Preprint, 2007. Available at SSRN 965265.
  • Osajima, Y., General asymptotics of Wiener functionals and application to implied volatilities, In Large Deviations and Asymptotic Methods in Finance, edited by P.K. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, and J. Teichmann, pp. 137–173, 2015 (Springer International Publishing: Cham).
  • Pham, H., Large deviations in mathematical finance, 2010. Available online at: https://www.lpsm.paris/pageperso/pham/GD-finance.pdf.
  • Sin, C.A., Complications with stochastic volatility models. Adv. Appl. Probab., 1998, 30(1), 256–268. doi: 10.1239/aap/1035228003