A Tale of Two Indices

Abstract

Pricing options involves a volatility input. Since volatility is not directly observable and it also varies stochastically over time, volatility risk is a significant concern for most option traders. Not surprisingly, then, there has always been considerable interest in the CBOE's VIX volatility index, although relatively little trading of derivatives based on it. The original VIX was a weighted average of Black-Scholes implied volatilities, which made it (in principle) a good estimator of future volatility, but hard to replicate with traded securities. The original VIX has been recently replaced by a new formula that is not model dependent. In this article, Carr and Wu review the old VIX (now called the VXO) and the new VIX and present a wide variety of results on their behavior. An interesting difference is that the new VIX, squared, is a good hedge for realized variance. This makes the new VIX a better underlier for volatility derivative contracts, which are now being launched into the marketplace by the CBOE. The article examines the performance of the two indices as forecasts of realized volatility, and shows how the VIX responds around an uncertainty diminishing information event, meetings of the Federal Open Market Committee. Carr and Wu also obtain interesting results on the market's volatility risk premium from direct measurement of risk neutral volatility in the VIX.