Linking Vanillas and VIX Options: A Constrained Martingale Optimal Transport Problem

21 Pages Posted: 19 Nov 2013 Last revised: 25 Apr 2015

See all articles by Stefano De Marco

Stefano De Marco

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Pierre Henry-Labordere

Natixis - Paris, France

Date Written: November 15, 2013

Abstract

VIX options traded on the CBOE have become popular volatility derivatives. As S&P500 vanilla options and VIX both depend on S&P500 volatility dynamics, it is important to understand the link between these products. In this paper, we bound VIX options from vanilla options and VIX futures. This leads us to introduce a new martingale optimal transportation problem that we solve numerically. Analytical lower and upper bounds are also provided which already highlight some (potential) arbitrage opportunities. We fully characterize the class of marginal distributions for which these explicit bounds are optimal, and illustrate numerically that they seem to be optimal for the market-implied marginal distributions.

Suggested Citation

De Marco, Stefano and Henry-Labordere, Pierre, Linking Vanillas and VIX Options: A Constrained Martingale Optimal Transport Problem (November 15, 2013). Available at SSRN: https://ssrn.com/abstract=2354898 or http://dx.doi.org/10.2139/ssrn.2354898

Stefano De Marco

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France

Pierre Henry-Labordere (Contact Author)

Natixis - Paris, France ( email )

Paris, Paris 75
France

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