Analysis of VIX Markets with a Time-Spread Portfolio

A. Papanicolaou

Research output: Contribution to journalArticlepeer-review


This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s 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.

Original languageEnglish (US)
Pages (from-to)374-408
Number of pages35
JournalApplied Mathematical Finance
Issue number5
StatePublished - Sep 2 2016


  • VIX options
  • model-free pricing
  • static hedging
  • stochastic volatility
  • time-spread portfolio

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics


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