Work

Path dependent optimal transport and model calibration on exotic derivatives

Year: 2021

Type: article

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 localisation result, which reduces the dimensionality of the solution by identifying appropriate 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.

Source: The Annals of Applied Probability

DOI: 10.1214/20-aap1617

Authors: Ivan Guo, Grégoire Loeper

Institution: Monash University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: BNP Paribas Cardif, Australian Research Council

Award: Liquidity in financial markets