Computational Aspects of Robust Optimized Certainty Equivalents and Option Pricing

23 Pages Posted: 29 May 2020

See all articles by Daniel Bartl

Daniel Bartl

University of Konstanz

Samuel Drapeau

China Academy of Financial Research (SAIF) and School of Mathematical Sciences

Ludovic Tangpi

Princeton University

Date Written: January 2020

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.

Keywords: average value‐at‐risk, convex duality, distribution uncertainty, optimized certainty equivalent, optimal transport, penalization, robust option pricing, Wasserstein distance

Suggested Citation

Bartl, Daniel and Drapeau, Samuel and Tangpi, Ludovic, Computational Aspects of Robust Optimized Certainty Equivalents and Option Pricing (January 2020). Mathematical Finance, Vol. 30, Issue 1, pp. 287-309, 2020, Available at SSRN: https://ssrn.com/abstract=3613893 or http://dx.doi.org/10.1111/mafi.12203

Daniel Bartl (Contact Author)

University of Konstanz

Samuel Drapeau

China Academy of Financial Research (SAIF) and School of Mathematical Sciences ( email )

Shanghai Jiao Tong University
211 West Huaihai Road
Shanghai, 200030
China

HOME PAGE: http://www.samuel-drapeau.info

Ludovic Tangpi

Princeton University

22 Chambers Street
Princeton, NJ 08544-0708
United States

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