Analysis of VIX Markets with a Time-Spread Portfolio

33 Pages Posted: 16 Jun 2015 Last revised: 5 Jun 2017

See all articles by Andrew Papanicolaou

Andrew Papanicolaou

North Carolina State University - Department of Mathematics

Date Written: June 4, 2017


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 a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure.

Keywords: Model-Free Pricing, Volatility Derivatives, VIX options

JEL Classification: G12, G13

Suggested Citation

Papanicolaou, Andrew, Analysis of VIX Markets with a Time-Spread Portfolio (June 4, 2017). Applied Mathematical Finance, (2016) Vol. 23, No. 5, pp. 374-408, NYU Poly Research Paper, Available at SSRN: or

Andrew Papanicolaou (Contact Author)

North Carolina State University - Department of Mathematics ( email )

Campus Box 8205
NC State University
Raleigh, NC 27695-8205
United States

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