Calibration of local‐stochastic volatility models by optimal transport. (9th August 2021)

• Record Type: Journal Article
• Authors: Guo, Ivan; Loeper, Grégoire; Wang, Shiyi
• Is Part Of: Mathematical finance. Volume 32:Number 1(2022)
• Page Start: 46
• Page End: 77
• Publication Date: 2021-08-09
• Subjects: optimal transport -- duality theory -- local‐stochastic volatility -- calibration; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12335
• Languages: English
• ISSNs: 0960-1627

Abstract

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 optimize our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimization 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.