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

DOI10.1137/140960724zbMath1386.91138OpenAlexW3123878280MaRDI QIDQ3456842

Stefano De Marco, Pierre Henry-Labordère

Publication date: 9 December 2015

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/31ac257c05bd370a959af21f1823b81836aad1ab

zbMATH Keywords

dualityVIX optionsmartingale optimal transportrobust sub/super-replication

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Linear programming (90C05) Semi-infinite programming (90C34) Derivative securities (option pricing, hedging, etc.) (91G20) Duality theory (optimization) (49N15)

Related Items (14)

Fine properties of the optimal Skorokhod embedding problem ⋮ Bounds for VIX futures given S{\&}P 500 smiles ⋮ Canonical supermartingale couplings ⋮ Pricing bounds for volatility derivatives via duality and least squares Monte Carlo ⋮ Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options ⋮ Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options ⋮ Perturbation analysis of sub/super hedging problems ⋮ Supermartingale Brenier's theorem with full-marginals constraint ⋮ Short Communication: Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures ⋮ Dispersion-constrained martingale Schrödinger problems and the exact joint S\&P 500/VIX smile calibration puzzle ⋮ A general framework for a joint calibration of VIX and VXX options ⋮ An explicit martingale version of the one-dimensional Brenier's theorem with full marginals constraint ⋮ Joint Modeling and Calibration of SPX and VIX by Optimal Transport ⋮ The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew

Cites Work

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• Model-independent bounds for option prices -- a mass transport approach
• Martingale optimal transport and robust hedging in continuous time
• Upper bounds on stop-loss premiums in case of known moments up to the fourth order
• Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS
• Stochastic Target Problems with Controlled Loss
• Optimal Transportation with Traffic Congestion and Wardrop Equilibria
• Extreme Points of Moment Sets
• Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model
• ROBUST BOUNDS FOR FORWARD START OPTIONS
• A CONSISTENT PRICING MODEL FOR INDEX OPTIONS AND VOLATILITY DERIVATIVES
• AUTOMATED OPTION PRICING: NUMERICAL METHODS
• Optimal transportation with capacity constraints
• The Existence of Probability Measures with Given Marginals

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