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Model-Free Implied Volatility: From Surface To Index

Author

Listed:
  • 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.

Suggested Citation

  • M. Fukasawa & I. Ishida & N. Maghrebi & K. Oya & M. Ubukata & K. Yamazaki, 2011. "Model-Free Implied Volatility: From Surface To Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 433-463.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:04:n:s0219024911006681
    DOI: 10.1142/S0219024911006681
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    References listed on IDEAS

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    1. Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," Economics Series Working Papers 2004-FE-20, University of Oxford, Department of Economics.
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    Cited by:

    1. Toshiaki Ogawa & Masato Ubukata & Toshiaki Watanabe, 2020. "Stock Return Predictability and Variance Risk Premia around the ZLB," IMES Discussion Paper Series 20-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    2. Fassas, Athanasios P. & Siriopoulos, Costas, 2021. "Implied volatility indices – A review," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 303-329.
    3. Masato Ubukata, 2023. "Variance Risk Premium Components in Japan for Predictability: Evidence from the COVID-19 Pandemic," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 15(8), pages 1-27, August.
    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.
    5. Masato Ubukata, 2022. "A time-varying jump tail risk measure using high-frequency options data," Empirical Economics, Springer, vol. 63(5), pages 2633-2653, November.
    6. Futeri Jazeilya Md Fadzil & John G. O’Hara & Wing Lon Ng, 2017. "Cross-sectional volatility index as a proxy for the VIX in an Asian market," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1364011-136, January.
    7. 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.
    8. 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.
    9. Hiroyuki Okawa, 2023. "Markov-Regime Switches in Oil Markets: The Fear Factor Dynamics," JRFM, MDPI, vol. 16(2), pages 1-20, January.
    10. Fabien Le Floc’h, 2018. "Variance Swap Replication: Discrete or Continuous?," JRFM, MDPI, vol. 11(1), pages 1-15, February.
    11. Kazuki Nagashima & Tsz-Kin Chung & Keiichi Tanaka, 2014. "Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 351-396, November.

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