Computational aspects of robust optimized certainty equivalents and option pricing

Daniel Bartl, Samuel Drapeau, Ludovic Tangpi

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Accounting for model uncertainty in risk management and option pricing leads to infinite-dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so-called optimized certainty equivalent (OCE) risk measure—including the average value-at-risk as a special case. First, we focus on the case where the uncertainty is modeled by a nonlinear expectation that penalizes distributions that are “far” in terms of optimal-transport distance (e.g. Wasserstein distance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite-dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value-at-risk is a tail risk measure.

Original languageEnglish (US)
Pages (from-to)287-309
Number of pages23
JournalMathematical Finance
Volume30
Issue number1
DOIs
StatePublished - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

Keywords

  • Wasserstein distance
  • average value-at-risk
  • convex duality
  • distribution uncertainty
  • optimal transport
  • optimized certainty equivalent
  • penalization
  • robust option pricing

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