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The Journal of Derivatives

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Article

New Approach to Estimating VIX Truncation Errors Using Corridor Variance Swaps

Desheng Wu and Tianxiang Liu
The Journal of Derivatives Summer 2018, 25 (4) 54-70; DOI: https://doi.org/10.3905/jod.2018.1.066
Desheng Wu
is a distinguished professor at the School of Economics and Management, University of Chinese Academy of Sciences, in China and a professor at Stockholm University in Sweden
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Tianxiang Liu
is a PhD Candidate at the School of Economics and Management, University of Chinese Academy of Sciences, in Beijing, China
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Abstract

The original VIX index (now called VXO) uses 8 at the money calls and puts to measure implied volatility for the S&P 100 Index at a 30-day maturity. The new VIX formula uses all out of the money calls and puts to implement a formula that, in principle, requires options with strike prices that span the full range of possible stock prices at expiration. No actual market lists strike prices over such a wide range. Even for options on a highly active and liquid index like the S&P 500, the most remote tails of the risk neutral density will be missing. Coverage of the tails can be very asymmetrical and it can vary quite a lot from period to period. The coverage in less active emerging markets is distinctly worse. Liu and Wu propose a way to estimate the resulting truncation error using corridor variance swaps. In the course of deriving it, they develop a new approach to pricing corridor variance swaps. Comparing estimates of the truncation error for the S&P 500 versus the Chinese ETF50, they find it is about 0.1 vol points for the S&P but 2.61 vol points in the Chinese market. Results are also reported for Mexico, Korea, India and Russia and show that in some cases significant truncation is present on one or both tails.

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The Journal of Derivatives: 25 (4)
The Journal of Derivatives
Vol. 25, Issue 4
Summer 2018
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New Approach to Estimating VIX Truncation Errors Using Corridor Variance Swaps
Desheng Wu, Tianxiang Liu
The Journal of Derivatives May 2018, 25 (4) 54-70; DOI: 10.3905/jod.2018.1.066

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New Approach to Estimating VIX Truncation Errors Using Corridor Variance Swaps
Desheng Wu, Tianxiang Liu
The Journal of Derivatives May 2018, 25 (4) 54-70; DOI: 10.3905/jod.2018.1.066
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  • Article
    • Abstract
    • LITERATURE REVIEW
    • METHODOLOGY
    • METHODOLOGY: CONNECTION BETWEEN VIX TRUNCATION ERROR AND CVS
    • METHODOLOGY: ESTIMATION OF VIX TRUNCATION ERROR AND CVS
    • SIMULATION
    • EMPIRICAL RESULTS: VIX TRUNCATION ERROR IN CHINA AND THE U.S.
    • TRUNCATION ERROR IN OTHER EMERGING MARKETS
    • CONCLUSION
    • REFERENCES
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