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Construction and Interpretation of Model-Free Implied Volatility

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  • Torben G. Andersen
  • Oleg Bondarenko

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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 School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-24.

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Length: 34
Date of creation: 17 Sep 2007
Date of revision:
Handle: RePEc:aah:create:2007-24

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Model-Free Implied Volatility; Corridor Implied Volatility; Realized Volatility; VIX; Volatility Forecasting; Risk-Neutral Density;

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References

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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  2. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Universite de Montreal, Departement de sciences economiques.
  3. Tim Bollerslev & Hao Zhou, 2006. "Expected stock returns and variance risk premia," Finance and Economics Discussion Series 2007-11, Board of Governors of the Federal Reserve System (U.S.).
  4. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October.
  5. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
  6. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
  7. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  8. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
  9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  10. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. Mark Britten-Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, 04.
  13. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  14. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
  15. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2004. "The Cross-Section of Volatility and Expected Returns," NBER Working Papers 10852, National Bureau of Economic Research, Inc.
  16. Whaley, Robert E, 1986. " Valuation of American Futures Options: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 41(1), pages 127-50, March.
  17. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  18. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  19. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
  20. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
  21. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
  22. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
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Citations

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Cited by:
  1. Leonidas Tsiaras, 2010. "The Forecast Performance of Competing Implied Volatility Measures: The Case of Individual Stocks," CREATES Research Papers 2010-34, School of Economics and Management, University of Aarhus.
  2. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
  3. 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.
  4. Fernandes, Marcelo & Medeiros, Marcelo C. & Scharth, Marcel, 2013. "Modeling and predicting the CBOE market volatility index," Textos para discussão 342, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  5. Thomas Busch & Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets," CREATES Research Papers 2007-09, School of Economics and Management, University of Aarhus.
  6. 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.
  7. 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.
  8. Andersen, Torben G. & Bondarenko, Oleg, 2014. "VPIN and the flash crash," Journal of Financial Markets, Elsevier, vol. 17(C), pages 1-46.
  9. 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.

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