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Calibration of Local-Stochastic Volatility Models by Optimal Transport

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  • Ivan Guo
  • Gregoire Loeper
  • Shiyi Wang

Abstract

In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimisation problem, for which we provide a PDE formulation along with its dual counterpart. Then we solve numerically the dual problem, which involves a fully non-linear Hamilton-Jacobi-Bellman equation. The method is tested by calibrating a Heston-like LSV model with simulated data and foreign exchange market data.

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  • Ivan Guo & Gregoire Loeper & Shiyi Wang, 2019. "Calibration of Local-Stochastic Volatility Models by Optimal Transport," Papers 1906.06478, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:1906.06478
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    File URL: http://arxiv.org/pdf/1906.06478
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    Cited by:

    1. Ivan Guo & Gregoire Loeper & Jan Obloj & Shiyi Wang, 2020. "Joint Modelling and Calibration of SPX and VIX by Optimal Transport," Papers 2004.02198, arXiv.org, revised Sep 2021.

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