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

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