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

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.