Bounds for VIX futures given S{\&}P 500 smiles
type: Item
instance of: scholarly article
title: Bounds for VIX futures given S{\&}P 500 smiles
zbMATH Open document ID: 1422.91698
author: Julien Guyon
author: Romain Menegaux
author: Marcel Nutz
published in: Finance and Stochastics
publication date: 2017-07-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1609.05832
review text: The authors study the problem of upper and lower bounds for future contracts having the popular VIX volatility index as underlying. Although the squared VIX may be replicated with calls and puts on S\&P500, VIX itself cannot, raising the need for sharp upper and lower bounds. This is typically done via affine payoff functions that produce a totally unsatisfactory zero lower bound. The authors exploit the classical duality approach to the problem which requires the proof of absence of a duality gap which is the main theoretical result of the paper. Since the replicating portfolio that arise from this approach are difficult to implement, the authors also develop what they call ``functionally generated portfolios'' which have an easier implementation and still produce a great improvement particularly for what concerns the lower bound on the VIX future.
reviewed by: Gianluca Cassese
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 49N05
zbMATH DE Number: 6751101
zbMATH Keywords: VIX futures
zbMATH Keywords: price bounds
zbMATH Keywords: model-free pricing
zbMATH Keywords: robust hedging
MaRDI profile type: Publication
OpenAlex ID: W2523334480
arXiv ID: 1609.05832
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DOI: 10.1007/S00780-017-0334-6
description: scientific article