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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.

Suggested Citation

  • Torben G. Andersen & Oleg Bondarenko, 2007. "Construction and Interpretation of Model-Free Implied Volatility," NBER Working Papers 13449, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:13449
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    1. 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, April.
    2. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    3. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    4. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    6. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    7. 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.
    8. Whaley, Robert E, 1986. " Valuation of American Futures Options: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 41(1), pages 127-150, March.
    9. 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.
    10. 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.
    11. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    12. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    13. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    14. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
    15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    16. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    17. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    18. 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.
    19. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross-Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    20. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
    21. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    22. 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 637-654, May-June.
    23. 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.
    24. 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 653-672, October.
    25. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, February.
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    Cited by:

    1. 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.
    2. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
    3. 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.
    4. 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.
    5. Barunik, Jozef & Barunikova, Michaela, 2015. "Revisiting the long memory dynamics of implied-realized volatility relation: A new evidence from wavelet band spectrum regression," FinMaP-Working Papers 43, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    6. Muzzioli, Silvia, 2015. "The optimal corridor for implied volatility: From periods of calm to turmoil," Journal of Economics and Business, Elsevier, vol. 81(C), pages 77-94.
    7. repec:eee:empfin:v:43:y:2017:i:c:p:59-73 is not listed on IDEAS
    8. 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.
    9. Birkelund, Ole Henrik & Haugom, Erik & Molnár, Peter & Opdal, Martin & Westgaard, Sjur, 2015. "A comparison of implied and realized volatility in the Nordic power forward market," Energy Economics, Elsevier, vol. 48(C), pages 288-294.
    10. Elyas Elyasani & Luca Gambarelli & Silvia Muzzioli, 2016. "The risk asymmetry index," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 16212, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    11. Andersen, Torben G. & Bondarenko, Oleg, 2014. "VPIN and the flash crash," Journal of Financial Markets, Elsevier, vol. 17(C), pages 1-46.
    12. repec:esx:essedp:713 is not listed on IDEAS
    13. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, Elsevier.
    14. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    15. Mencía, Javier & Sentana, Enrique, 2015. "Volatility-related exchange traded assets: an econometric investigation," CEPR Discussion Papers 10444, C.E.P.R. Discussion Papers.
    16. Kian-Guan Lim & Christopher Ting, 2012. "The term structure of S&P 100 model-free volatilities," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1041-1058, November.
    17. 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.
    18. Michael O'Neill & Kent Wang & Zhangxin (Frank) Liu & Tom Smith, 2016. "A State-Price Volatility Index for China's Stock Market," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 56(3), pages 607-626, September.
    19. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    20. Maria Gonzalez-Perez & Alfonso Novales, 2011. "The information content in a volatility index for Spain," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(2), pages 185-216, June.
    21. Dew-Becker, Ian & Giglio, Stefano & Le, Anh & Rodriguez, Marius, 2017. "The price of variance risk," Journal of Financial Economics, Elsevier, vol. 123(2), pages 225-250.
    22. Kiesel, Rüdiger & Rahe, Florentin, 2017. "Option pricing under time-varying risk-aversion with applications to risk forecasting," Journal of Banking & Finance, Elsevier, vol. 76(C), pages 120-138.
    23. Ohnsorge,Franziska Lieselotte & Stocker,Marc & Some,Modeste Y., 2016. "Quantifying uncertainties in global growth forecasts," Policy Research Working Paper Series 7770, The World Bank.
    24. Gonzalez-Perez, Maria T., 2015. "Model-free volatility indexes in the financial literature: A review," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 141-159.

    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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