Conclusion

Chapter
Part of the Springer Finance book series (FINANCE)

Abstract

As the time now comes to summarise and assess this presentation of ACE, let us first recall our original mandate. Our intention was to establish an explicit and non-arbitrable connection between some of the SV model classes, which are capable of describing the joint dynamics of an underlying and of its associated European options. That connection could be approximate, provided that its precision was known and if possible controllable. We also demanded a generic treatment in terms of covered models, and were aiming for some practical, efficient algorithm. We now offer our views on which of these objectives have been attained, and on which still remain open subjects.

Keywords

Explosive Volatility Vanilla Hedging 

References

  1. 1.
    Durrleman, V.: From limplied to spot volatilities. Ph.D. thesis, Princeton University (2003)Google Scholar
  2. 2.
    Dupire, B.: Pricing with a smile. Risk 7(1), 18–20 (1994)Google Scholar
  3. 3.
    Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward. D.E.: Managing smile risk. Wilmott, pp. 84–108 (2002)Google Scholar
  4. 4.
    Fournie, E., Lebuchoux, J., Touzi, N.: Small noise expansion and importance sampling. Asymptot Anal. 14(4), 361–376 (1997)MATHMathSciNetGoogle Scholar
  5. 5.
    Piterbarg, V.V.: Markovian projection for volatility calibration. Risk Magazine, vol. 20, 84–89 (2007)Google Scholar
  6. 6.
    Hafner, R.: Stochastic implied volatility. Lecture Notes in Economics and Mathematical Systems, vol. 545. Springer, Berlin (2004)Google Scholar
  7. 7.
    Andersen, L.B.G., Piterbarg, V.V.: Moment explosions in stochastic volatility models. Finance Stochast. 11(9), 29–50 (2006)Google Scholar
  8. 8.
    Kunitomo, N., Takahashi, A.: Applications of the asymptotic expansion approach based on Malliavin-Watanabe calculus in financial problems. University of Tokyo, Graduate School of Mathematical Sciences, Report (2003)Google Scholar
  9. 9.
    Medvedev, A.: Asymptotic methods for computing implied volatilities under stochastic volatility. Technical report, National Center of Competence in Research (2004)Google Scholar
  10. 10.
    Osajima, Y.: General asymptotics of Wiener functionals and application to mathematical finance. University of Tokyo, Graduate school of mathematical sciences, Report (2007)Google Scholar
  11. 11.
    Benhamou, E., Gobet, E., Miri, M.: Expansion formulas for European options in a local volatility model. Forthcoming Int. J. Theor. Appl. Finance 13, 603 (2010)Google Scholar
  12. 12.
    Lee, R.W.: The moment formula for implied volatility at extreme strikes. Math. Financ. 14(3), 469–480 (2004)Google Scholar
  13. 13.
    Carmona, R., Nadtochiy, S.: An infinite dimensional stochastic analysis approach to local volatility models. Commun. Stoch. Anal 2(1), 109–123 (2008)MathSciNetGoogle Scholar
  14. 14.
    Carmona, R., Nadtochiy, S.: Local volatility dynamic models. Finance Stochast. 13(1), 1–48 (2009)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.LondonUK

Personalised recommendations