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Revisiting the fractional cointegrating dynamics of implied-realized volatility relation with wavelet band spectrum regression

  • Jozef Barunik
  • Michaela Barunikova

This paper revisits the fractional cointegrating relationship between ex-ante implied volatility and ex-post realized volatility. We argue that the concept of corridor implied volatility (CIV) should be used instead of the popular model-free option-implied volatility (MFIV) when assessing the fractional cointegrating relation as the latter may introduce bias to the estimation. For the realized volatility, we use recently proposed methods which are robust to noise as well as jumps and interestingly we find that it does not affect the implied-realized volatility relation. In addition, we develop a new tool for the estimation of fractional cointegrating relation between implied and realized volatility based on wavelets, a wavelet band least squares (WBLS). The main advantage of WBLS in comparison to other frequency domain methods is that it allows us to work conveniently with potentially non-stationary volatility due to the properties of wavelets. We study the dynamics of the relationship in the time-frequency domain with the wavelet coherence confirming that the dependence comes solely from the lower frequencies of the spectra. Motivated by this result we estimate the relationship only on this part of the spectra using WBLS and compare our results to the fully modified narrow-band least squares (FMNBLS) based on the Fourier frequencies. In the estimation, we use the S&P 500 and DAX monthly and bi-weekly option prices covering the recent financial crisis and we conclude that in the long-run, volatility inferred from the option prices using the corridor implied volatility (CIV) provides an unbiased forecast of the realized volatility.

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Paper provided by in its series Papers with number 1208.4831.

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Date of creation: Aug 2012
Date of revision: Feb 2013
Handle: RePEc:arx:papers:1208.4831
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  12. Baruník, Jozef & Vácha, Lukáš, 2014. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," FinMaP-Working Papers 16, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
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  24. Jozef Barunik & Tomas Krehlik & Lukas Vacha, 2012. "Modeling and forecasting exchange rate volatility in time-frequency domain," Papers 1204.1452,, revised Feb 2015.
  25. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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