Bounds for VIX futures given S&P 500 smiles

Julien Guyon (), Romain Menegaux () and Marcel Nutz ()
Additional contact information
Julien Guyon: Bloomberg L.P.
Romain Menegaux: Bloomberg L.P.
Marcel Nutz: Columbia University

Finance and Stochastics, 2017, vol. 21, issue 3, No 1, 593-630

Abstract: Abstract We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of minimizing/maximizing certain risk-neutral expectations is introduced and shown to yield the same value. The classical bounds for VIX futures given the smiles only use a calendar spread of log-contracts on the S&P 500. We analyze for which smiles the classical bounds are sharp and how they can be improved when they are not. In particular, we introduce a family of functionally generated portfolios which often improves the classical bounds while still being tractable; more precisely, they are determined by a single concave/convex function on the line. Numerical experiments on market data and SABR smiles show that the classical lower bound can be improved dramatically, whereas the upper bound is often close to optimal.

Keywords: VIX futures; Price bounds; Model-free pricing; Robust hedging; 91B25; 60G42; 49N05 (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00780-017-0334-6

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