Calibration of Local-Stochastic Volatility Models by Optimal Transport

Ivan Guo, Gregoire Loeper and Shiyi Wang

Papers from arXiv.org

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.

Date: 2019-06, Revised 2021-07
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1906.06478

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