Gauging the Investor Fear Gauge: Implementation Problems of the Cboe's New Volatility Index

55 Pages Posted: 26 Mar 2005 Last revised: 21 Feb 2013

See all articles by George J. Jiang

George J. Jiang

Washington State University

Yisong S. Tian

York University - Schulich School of Business

Date Written: March 12, 2005

Abstract

Recently, the Chicago Board Options Exchange (CBOE) redesigned its widely followed stock market volatility index (VIX). Instead of tracking the Black-Scholes implied volatility of at-the-money options, it is now based on the theoretically superior model-free implied volatility. In this paper, we analyze the CBOE's implementation of the new VIX and find economically significant discretization and truncation errors in its calculation. Based on the simulated prices of S&P 500 index options at the listed strike prices on a typical trading day, we find that the CBOE calculation may overestimate the true volatility by as much as 79 basis points or underestimate it by as much as 198 basis points. As each basis point is equivalent to $10 per VIX futures contract, these errors are clearly economically significant. To fix the implementation problem, we propose an alternative method, called the no-arbitrage smoothing method, for calculating the new VIX. Based on the construction of the implied volatility function, our method is straightforward to implement and corrects both types of errors in the CBOE calculation. The accuracy and robustness of our method is strongly supported by the results of both Monte Carlo simulation and empirical implementation using daily data of S&P 500 index options.

Keywords: Volatility index, VIX, Investor fear gauge, Volatility smile, Fair value of future variance, Model-free implied volatility, No-arbitrage smoothing

JEL Classification: G13, G14

Suggested Citation

Jiang, George and Tian, Yisong Sam, Gauging the Investor Fear Gauge: Implementation Problems of the Cboe's New Volatility Index (March 12, 2005). Available at SSRN: https://ssrn.com/abstract=685503 or http://dx.doi.org/10.2139/ssrn.685503

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 Sam 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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