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Construction and Interpretation of Model-Free Implied Volatility

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  • Torben G. Andersen
  • Oleg Bondarenko

Abstract

The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the VIX index is computed through a tail-truncation which renders it more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and hence estimate the corresponding volatility measures, under the standard Black-Scholes model. Finally, we undertake the first empirical exploration of the CIV measures in the literature. Our results indicate that the measure can help us refine and systematize the information embedded in the derivatives markets. As such, the CIV measure may serve as a tool to facilitate empirical analysis of both volatility forecasting and volatility risk pricing across distinct future states of the world for diverse asset categories and time horizons.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13449.

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Date of creation: Sep 2007
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Handle: RePEc:nbr:nberwo:13449

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Cited by:
  1. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
  2. Tzang, Shyh-Weir & Hung, Chih-Hsing & Wang, Chou-Wen & Shyu, David So-De, 2011. "Do liquidity and sampling methods matter in constructing volatility indices? Empirical evidence from Taiwan," International Review of Economics & Finance, Elsevier, vol. 20(2), pages 312-324, April.
  3. Torben G. Andersen & Oleg Bondarenko, 2011. "VPIN and the Flash Crash," CREATES Research Papers 2011-50, School of Economics and Management, University of Aarhus.
  4. Aragon, George O. & Spencer Martin, J., 2012. "A unique view of hedge fund derivatives usage: Safeguard or speculation?," Journal of Financial Economics, Elsevier, vol. 105(2), pages 436-456.
  5. Fernandes, Marcelo & Medeiros, Marcelo C. & Scharth, Marcel, 2014. "Modeling and predicting the CBOE market volatility index," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 1-10.
  6. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
  7. Tsiaras, Leonidas, 2009. "The Forecast Performance of Competing Implied Volatility Measures: The Case of Individual Stocks," Finance Research Group Working Papers F-2009-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  8. Sheri M. Markose & Yue Peng & Amadeo Alentorn, 2012. "Forecasting Extreme Volatility of FTSE-100 With Model Free VFTSE, Carr-Wu and Generalized Extreme Value (GEV) Option Implied Volatility Indices," Economics Discussion Papers 713, University of Essex, Department of Economics.
  9. Maria Gonzalez-Perez & Alfonso Novales, 2011. "The information content in a volatility index for Spain," SERIEs, Spanish Economic Association, vol. 2(2), pages 185-216, June.

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