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June 2021 Path dependent optimal transport and model calibration on exotic derivatives
Ivan Guo, Grégoire Loeper
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Ann. Appl. Probab. 31(3): 1232-1263 (June 2021). DOI: 10.1214/20-AAP1617

Abstract

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path dependent partial differential equations (PPDEs). Moreover, we provide a dimension reduction result based on the new notion of “semifiltrations”, which identifies appropriate Markovian state variables based on the constraints and the cost function. Our technique is then applied to the exact calibration of volatility models to the prices of general path dependent derivatives.

Funding Statement

The authors are part of the Monash Centre for Quantitative Finance and Investment Strategies, which has been supported by BNP Paribas. I. Guo has been partially supported by the Australian Research Council (Grant DP170101227).

Acknowledgments

The authors would like to thank Ben Goldys and the anonymous referee for their valuable comments and suggestions.

Citation

Download Citation

Ivan Guo. Grégoire Loeper. "Path dependent optimal transport and model calibration on exotic derivatives." Ann. Appl. Probab. 31 (3) 1232 - 1263, June 2021. https://doi.org/10.1214/20-AAP1617

Information

Received: 1 June 2019; Revised: 1 August 2020; Published: June 2021
First available in Project Euclid: 23 June 2021

Digital Object Identifier: 10.1214/20-AAP1617

Subjects:
Primary: 60H30 , 91G80
Secondary: 93E20

Keywords: Optimal transport , path dependent PDE , volatility calibration

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 3 • June 2021
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