From Bachelier to Dupire via optimal transport

Mathias Beiglböck (), Gudmund Pammer () and Walter Schachermayer ()
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Mathias Beiglböck: Universität Wien
Gudmund Pammer: ETH Zürich
Walter Schachermayer: Universität Wien

Finance and Stochastics, 2022, vol. 26, issue 1, No 4, 59-84

Abstract: Abstract Famously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

Keywords: Bachelier; Dupire’s formula; Kellerer’s theorem; Optimal transport; Martingales; Peacocks; 60G20 (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-021-00466-3

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