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Extracting Model-Free Volatility from Option Prices: An Examination of the VIX Index

41 Pages Posted: 8 Feb 2006 Last revised: 1 May 2014

George J. Jiang

Washington State University

Yisong S. Tian

York University - Schulich School of Business

Date Written: Januarty 8, 2007

Abstract

The Chicago Board Options Exchange (CBOE) recently redesigned its widely followed VIX volatility index. While the new VIX is conceptually more appealing than its predecessor, the CBOE's implementation of the index is flawed. Using option prices simulated under typical market conditions, we show that the CBOE procedure may underestimate the true volatility by as much as 198 index basis points or overestimate it by as much as 79 index basis points. As each index basis point is worth $10 per VIX futures contract, these errors are economically significant. More importantly, these errors exhibit predictable patterns in relations to volatility levels. We propose a simple solution to fix the problems, based on a smooth interpolation-extrapolation of the implied volatility function. This alternative method is accurate and robust across a wide range of model specifications and market conditions.

Keywords: volatility index, VIX, investor fear gauge, volatility smile, fair value of future variance, model-free implied volatility

JEL Classification: G13, G14

Suggested Citation

Jiang, George J. and Tian, Yisong S., Extracting Model-Free Volatility from Option Prices: An Examination of the VIX Index (Januarty 8, 2007). Journal of Derivatives, Vol. 14, No. 3, 2007. Available at SSRN: https://ssrn.com/abstract=880459 or http://dx.doi.org/10.2139/ssrn.880459

George Jiang

Washington State University ( email )

Department of Finance and Management Science
Carson College of Business
Pullman, WA 99-4746164
United States
509-3354474 (Phone)

HOME PAGE: http://directory.business.wsu.edu/bio.html?username=george.jiang

Yisong Tian (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada
416-736-2100, ext 77943 (Phone)
416-736-5687 (Fax)

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