We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a...

This article explores the relationship between option markets for the S&P500 (SPX) and CBOE's Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides...

This paper shows how to recover stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore they are better-suited for pricing VIX futures and derivatives. But the VIX itself is a...

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM), and can be tracked using Bayesian filtering. However, derivative data can be...

Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies examine whether there is significantly greater risk premium in VIX option...