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
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
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