Advertisement

Estimating Quadratic Variation Under Jumps and Micro-market Noise

  • Naoto Kunitomo
  • Seisho Sato
  • Daisuke Kurisu
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

We consider the estimation of quadratic variation of It\(\hat{o}\)’s semi-martingales with jumps, which is an extension of volatility estimation in previous chapters. The SIML estimation gives reasonable estimation results of quadratic variation with jumps since it has desirable asymptotic properties such as consistency and asymptotic normality.

References

  1. Cont, R., and P. Tankov. 2004. Financial modeling with jump processes. Chapman and Hall.Google Scholar
  2. Ikeda, N., and S. Watanabe. 1989. Stochastic differential equations and diffusion processes, 2nd ed. North-Holland.Google Scholar
  3. Jacod, J., and P. Protter. 2012. Discretization of processes. Berlin: Springer.Google Scholar
  4. Kurisu, D. 2017. Power variations and testing for co-jumps: the small noise approach. Scandinavian Journal of Statistics. http://onlinelibrary.wiley.com/doi/10.1111/sjos.12309/abstract.

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.School of Political Science and EconomicsMeiji UniversityTokyoJapan
  2. 2.Graduate School of EconomicsThe University of TokyoBunkyo-kuJapan
  3. 3.School of EngeneeringTokyo Institute of TechnologyTokyoJapan

Personalised recommendations