Discrete sine transform for multi-scale realized volatility measures§
In this study we present a new realized volatility estimator based on a combination of the multi-scale regression and discrete sine transform (DST) approaches. Multi-scale estimators similar to that recently proposed by Zhang (2006) can, in fact, be constructed within a simple regression-based approach by exploiting the linear relation existing between the market microstructure bias and the realized volatilities computed at different frequencies. We show how such a powerful multi-scale regression approach can also be applied in the context of the Zhou [ Nonlinear Modelling of High Frequency Financial Time Series , pp. 109--123, 1998] or DST orthogonalization of the observed tick-by-tick returns. Providing a natural orthonormal basis decomposition of observed returns, the DST permits the optimal disentanglement of the volatility signal of the underlying price process from the market microstructure noise. The robustness of the DST approach with respect to the more general dependent structure of the microstructure noise is also shown analytically. The combination of the multi-scale regression approach with DST gives a multi-scale DST realized volatility estimator similar in efficiency to the optimal Cramer--Rao bounds and robust against a wide class of noise contamination and model misspecification. Monte Carlo simulations based on realistic models for price dynamics and market microstructure effects show the superiority of DST estimators over alternative volatility proxies for a wide range of noise-to-signal ratios and different types of noise contamination. Empirical analysis based on six years of tick-by-tick data for the S&P 500 index future, FIB 30, and 30 year U.S. Treasury Bond future confirms the accuracy and robustness of DST estimators for different types of real data. §Earlier versions of this paper were circulated under the title ‘A discrete sine transform approach for realized volatility measurement’.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 12 (2012)
Issue (Month): 2 (April)
|Contact details of provider:|| Web page: http://www.tandfonline.com/RQUF20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/RQUF20|
When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:12:y:2012:i:2:p:263-279. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)
If references are entirely missing, you can add them using this form.