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Real-time estimation scheme for the spot cross volatility of jump diffusion processes

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  • Ogawa, Shigeyoshi
  • Ngo, Hoang-Long

Abstract

Given a finite set of observed data {Xtk(ω0),Ytk(ω0)} of just one sample path at n regularly spaced time of the processes Xt and Yt satisfying dXt=a0(t)dt+a1(t)dW1(t)+a2(t)dW2(t)+dJ1(t),dYt=b0(t)dt+b1(t)dW1(t)+b2(t)dW2(t)+dJ2(t),t∈[0,T], where J1,J2 are jump process, we are to investigate a numerical scheme for the estimation of the value νX,Y(t)=a1(t)b1(t)+a2(t)b2(t) called cross volatility. Our framework also contains the volatility estimation problem as a special case. We will show that our scheme works under mild assumptions on the activity of the jump process Jt.

Suggested Citation

  • Ogawa, Shigeyoshi & Ngo, Hoang-Long, 2010. "Real-time estimation scheme for the spot cross volatility of jump diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1962-1976.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:9:p:1962-1976
    DOI: 10.1016/j.matcom.2010.01.009
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    References listed on IDEAS

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    1. Jean Jacod, 2000. "Non‐parametric Kernel Estimation of the Coefficient of a Diffusion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 83-96, March.
    2. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    3. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
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    Cited by:

    1. Nien-Lin Liu & Hoang-Long Ngo, 2014. "Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis," Papers 1409.2214, arXiv.org.

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