Joint Modeling and Calibration of SPX and VIX by Optimal Transport

DOI10.1137/20M1375905zbMath1482.91203arXiv2004.02198OpenAlexW4206469263MaRDI QIDQ5019589

Shiyi Wang, Ivan Guo, Jan Obłój, Grégoire Loeper

Publication date: 10 January 2022

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

Full work available at URL: https://arxiv.org/abs/2004.02198

zbMATH Keywords

Hamilton-Jacobi-Bellman equationcalibrationoptimal transportstochastic volatility modelsoption pricesduality in optimal control

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Numerical methods involving duality (49M29) Applications of stochastic analysis (to PDEs, etc.) (60H30) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (6)

Empirical analysis of rough and classical stochastic volatility models to the SPX and VIX markets ⋮ Signature-Based Models: Theory and Calibration ⋮ Volatility is (mostly) path-dependent ⋮ MARKOVIAN STOCHASTIC VOLATILITY WITH STOCHASTIC CORRELATION — JOINT CALIBRATION AND CONSISTENCY OF SPX/VIX SHORT-MATURITY SMILES ⋮ Dispersion-constrained martingale Schrödinger problems and the exact joint S\&P 500/VIX smile calibration puzzle ⋮ The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew

Uses Software

• L-BFGS

Cites Work

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• Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients
• Model-independent bounds for option prices -- a mass transport approach
• Mimicking an Itō process by a solution of a stochastic differential equation
• Optimal transportation under controlled stochastic dynamics
• The reconstruction problem for the Euler-Poisson system in cosmology
• On the limited memory BFGS method for large scale optimization
• Mimicking the one-dimensional marginal distributions of processes having an Ito differential
• Pricing bounds for volatility derivatives via duality and least squares Monte Carlo
• 2017 MATRIX annals
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Path dependent optimal transport and model calibration on exotic derivatives
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• Semi-Lagrangian schemes for linear and fully non-linear diffusion equations
• Linking Vanillas and VIX Options: A Constrained Martingale Optimal Transport Problem
• Market completion using options
• Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
• Calibrating volatility surfaces via relative-entropy minimization
• Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options
• Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model
• Preconditioning the Augmented Lagrangian Method for Instationary Mean Field Games with Diffusion
• Regime-switching stochastic volatility model: estimation and calibration to VIX options
• An unconditionally monotone numerical scheme for the two-factor uncertain volatility model
• A CONSISTENT PRICING MODEL FOR INDEX OPTIONS AND VOLATILITY DERIVATIVES
• On VIX futures in the rough Bergomi model
• Short Communication: Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures
• Inversion of convex ordering in the VIX market
• A regime-switching Heston model for VIX and S&P 500 implied volatilities
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• ADI finite difference schemes for option pricing in the Heston model with correlation

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