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Model-Free Implied Volatility: From Surface To Index

  • 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)

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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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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