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Extracting Model-Free Volatility from Option Prices

An Examination of the VIX Index

George J. Jiang and Yisong S. Tian
The Journal of Derivatives Spring 2007, 14 (3) 35-60; DOI: https://doi.org/10.3905/jod.2007.681813
George J. Jiang
An assistant professor of finance at Eller College of Management, University of Arizona in Tucson, AZ.
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  • For correspondence: gjiang@eller.arizona.edu
Yisong S. Tian
An associate professor of finance at Schulich School of Business, York University in Toronto, Ontario, Canada.
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  • For correspondence: ytian@schulich.yorku.ca
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Abstract

The CBOE's VIX index is a measure of the implied volatility (IV) in 30-day stock index options. Originally constructed as a weighted average of Black-Scholes IVs from 8 at the money calls and puts, the VIX was redesigned in 2003. The new VIX uses a nonparametric procedure to extract an IV from out of the money calls and puts over the full range of strikes. Implementation of the theoretical procedure, however, requires several approximations, for example to deal with the fact that only a discrete set of strikes are traded in the market, rather than a continuum over the full range from zero to infinity, as required by the theory. In this article, Jiang and Tian look carefully at the new VIX algorithm to assess the impact of these approximations on its accuracy. They find that some of them may produce substantial errors, even in simply recovering the volatility input from a set of options in a pure Black-Scholes world. They then propose a modified calculation technique using a smoothing algorithm, that can almost entirely eliminate the errors.

TOPICS: Options, statistical methods, risk management

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Extracting Model-Free Volatility from Option Prices
George J. Jiang, Yisong S. Tian
The Journal of Derivatives Feb 2007, 14 (3) 35-60; DOI: 10.3905/jod.2007.681813

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Extracting Model-Free Volatility from Option Prices
George J. Jiang, Yisong S. Tian
The Journal of Derivatives Feb 2007, 14 (3) 35-60; DOI: 10.3905/jod.2007.681813
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