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Julien Guyon

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36
Date
2022/07/17
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6
Job
New York University | Adjunct Professor
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I finally found the time to write this article on Dispersion-Constrained Martingale Schrödinger Bridges and the Joint Entropic Calibration of Stochastic Volatility Models to S&P 500 and VIX Smiles. I remember presenting the results at the BFS One World Seminar Talk Series on July 16, 2020, exactly 2 years ago. Better late than never!In this article we extend our Schrödinger problem approach of the joint calibration problem [Guyon, J.: The Joint S&P 500/VIX Smile Calibration Puzzle Solved, Risk, April 2020] to continuous time: among all the (arbitrage-free) jointly calibrating semimartingale models, we build the one that minimizes the relative entropy with respect to a reference stochastic volatility (SV) model. This naturally leads to "Dispersion-constrained martingale Schrödinger bridges'', a new type of Schrödinger bridges which are constrained by the martingality of the SPX and by the prices of VIX derivatives.The calibrated model is identical to the reference model, but for an extra drift in the SV which, by duality, is written explicitly. The dual formulation consists of solving Hamilton-Jacobi-Bellman PDEs and maximizing a concave functional of those solutions over SPX and VIX payoffs. We show that the gradient of this dual functional simply reads as the difference between model and market prices, and therefore can be easily computed using classical finite difference methods. The dual maximization can then be performed by classical least squares techniques. Interestingly, the extra drift in SV is path-dependent in both the SPX and the instantaneous volatility. Numerical results on model-generated data illustrate the accuracy of the method.I would like to dedicate this article to the memory of my friend and colleague Marco Avellaneda, who was a pioneer in minimum entropy calibration.Comments welcome!#quantitativefinance #quantitativeresearch #sp500 #vix #calibrat
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Integromat
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https://www.linkedin.com/feed/update/urn:li:activity:6954476721299443712
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3
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Post
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https://www.linkedin.com/in/julien-guyon-9a5473b/
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