Path dependent optimal transport and model calibration on exotic derivatives

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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.

Original languageEnglish
Pages (from-to)1232-1263
Number of pages32
JournalAnnals of Applied Probability
Volume31
Issue number3
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Optimal transport
  • Path dependent PDE
  • Volatility calibration

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