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Model-Free Implied Volatility: From Surface To Index

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  • M. FUKASAWA

    ()
    (Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan)

  • I. ISHIDA

    ()
    (Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan)

  • N. MAGHREBI

    ()
    (Graduate School of Economics, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan)

  • K. OYA

    ()
    (Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka 560-0043, Japan)

  • M. UBUKATA

    ()
    (Department of Economics, Kushiro Public University of Economics, 4-1-1 Ashino, Kushiro, Hokkaido 085-8585, Japan)

  • K. YAMAZAKI

    ()
    (Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan)

Abstract

We propose a new method for approximating the expected quadratic variation of an asset based on its option prices. The quadratic variation of an asset price is often regarded as a measure of its volatility, and its expected value under pricing measure can be understood as the market's expectation of future volatility. We utilize the relation between the asset variance and the Black-Scholes implied volatility surface, and discuss the merits of this new model-free approach compared to the CBOE procedure underlying the VIX index. The interpolation scheme for the volatility surface we introduce is designed to be consistent with arbitrage bounds. We show numerically under the Heston stochastic volatility model that this approach significantly reduces the approximation errors, and we further provide empirical evidence from the Nikkei 225 options that the new implied volatility index is more accurate in predicting future volatility.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 14 (2011)
Issue (Month): 04 ()
Pages: 433-463

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Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:04:p:433-463

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Keywords: Model-free implied volatility index; volatility forecasting; volatility surface; variance swaps;

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Cited by:
  1. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX," Documentos de Trabajo del ICAE 2011-17, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Masato Ubukata & Toshiaki Watanabe, 2011. "Market Variance Risk Premiums in Japan as Predictor Variables and Indicators of Risk Aversion," Global COE Hi-Stat Discussion Paper Series gd11-214, Institute of Economic Research, Hitotsubashi University.
  4. Masato Ubukata & Toshiaki Watanabe, 2014. "Market variance risk premiums in Japan for asset predictability," Empirical Economics, Springer, vol. 47(1), pages 169-198, August.

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