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Rate efficient estimation of realized Laplace transform of volatility with microstructure noise

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  • Li Wang
  • Zhi Liu
  • Xiaochao Xia

Abstract

In this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0,T] using high‐frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We use the pre‐averaging approach to deal with the effect of microstructure noise. Under the high‐frequency scenario, we obtain a consistent estimator whose convergence rate is Δn−1/4, which is known as the optimal convergence rate of the estimation of integrated volatility functionals under the presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite‐sample performance of the proposed estimator.

Suggested Citation

  • Li Wang & Zhi Liu & Xiaochao Xia, 2019. "Rate efficient estimation of realized Laplace transform of volatility with microstructure noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(3), pages 920-953, September.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:3:p:920-953
    DOI: 10.1111/sjos.12365
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